Anode Overvoltage
Overpotential or Overvoltage refers to the excess electrical potential over theoretical potential at which the desired element is discharged at the electrode surface.
It will obviously vary with the different anode materials. It also varies from electrolyte to electrolyte given a fixed anode material. It also varies with current density, age, temperature etc. For Chlorate making we would like an Anode with a low Chlorine overpotential and a higher Oxygen overpotential. Because Amateur Chlorate cells are (usually) not pH controlled, we also need an Anode material with a low overpotential for the Oxidation of Hypochlorite ion.
For Perchlorate making we want a material with a low potential for the 'discharge of the Perchlorate ion' and a high Oxygen overpotential. The higher the Oxygen overpotential the better because it means that Oxygen will not be made at the Anode. Oxygen forming at the Anode is a leakage current we do not want and is one of the reasons for not getting 100% current efficiency when making Chlorate or Perchlorate. It also wears the Anode. Flourine raises the Oxygen overpotential at Lead Dioxide anodes.

Catalytic activity of Anode material
When making Chlorate in a non pH controlled cell, Chlorate is produced at the Anode surface by Oxidation of Hypochlorite ion to Chlorate (also known as 'Anodic Chlorate formation', or 'Making Chlorate by electricity', see Cell Chem. section). In industrial cells a different reaction takes place in the bulk of the solution (after Chlorine is produced at the Anode) as the pH is favourable for the appropriate species to be present in the proper ratio in the liquid for these so called 'bulk' reactions (also known as 'Chemical Chlorate formation') to happen.
In industry the Anodic Oxidation of Hypochlorite is very undesirable and is avoided. In amateur non-pH controlled cells it is the way all the Chlorate gets produced. The Anode material must therefor have catalytic activity for the evolution of Cl- and in addition to this must have catalytic activity for the Oxidation of Hypohlorite ion in the non-pH controlled Chlorate cell.
Magnetite has poor to zero activity for the Oxidation of Hypochlorite ion. Pt, C, MMO and MnO2 are OK. PbO2 is not very good AFAICS.
In the Perchlorate cell things are more complicated.

Cell Anodes
Material Comments
Graphite or Carbon Graphite is a dense form of the element Carbon. The terms Graphite and Carbon are sometimes used interchangeably.
Dense Graphite is much better than Carbon (softer and more porous than Graphite) as far as erosion is concerned.
Graphite or Carbon can be make to last longer by impregnating it with Linseed oil or some other substance to plug pores in order to decrease shredding. Dense Graphite cannot be impregnated with the oil. Proper pH control of the cell is of huge significance in regards to erosion too.
Carbon can be purchased at welding supply shops in the form of Gouging rods, and it is very advantageous to treat them with Linseed oil or other products, to make them last longer as they are very porous.
Gouging rods are manufactured in various ways and may even contain Iron particles. That may be good for gouging, not so good for Chlorate making.
Dense Graphite can be purchased at engineering supply shops where it is used in EDM's (Electro Discharge Machines).
Carbon rods from dry cell batteries can also be used. A large Graphite art pensil can also be used successfully.
Industrial users of Graphite keep the temperature below 40°C, Chloride concentration above 100g/l and current density between 33 & 43 mA per square cm.
It should be noted that as Graphite rods erode their surface area gets less and less. Therefor the current density will increase as will erosion. Bear this in mind when using Graphite rods.
Controlling the pH of the cell will have a huge influence on erosion. Figures from Industry regarding Graphite erosion are very impressive, being as low as 4 kg per Ton Sodium Chlorate (4 grams per kg Na Chlorate).
There is information regarding pH controlled amateur cells in the 'Graphite Anode' section below. The big Anode killers are high pH and a Chloride concentration below 30 grams per liter.

Graphite will NOT make Perchlorate in any sensible fashion, (unless in a cell with a diaphragm?).

Lead Dioxide A good Lead Dioxide Anode will last a long time and it is not effected by high temperature's (within reason, below 55C) or low Chloride levels. If Chloride levels get low in the Chlorate cell (approximately 50g per Liter Chloride), Perchlorate will start to form. You should not use Chromate additive with a Lead Dioxide Anode which in turn means that you should not use some types of Stainless Steel as they may corrode a small amount and introduce small amounts of Chromate into the electrolyte, 316 is OK. Chromate's lower current efficiency by forming a thin layer on the surface of the Anode. Anode current densities of 80mA to 300mA per square cm can be used. The lower current densitys are used in Chlorate cells as current efficiency will suffer if a high current density is used. High current densitys do not effect current efficiency in Perchlorate cells, in fact it improves CE.
Lead Dioxide is the HOLY GRAIL of Anodes. It can be let run and run until all Chloride has turned to Perchlorate which saves a great amount of labour. The Ti substrate Anode is the way forward for LD Anodes. Do not use Fluoride additive with Titanium Substrate Anodes.

Platinum Platinum is good but is expensive. It will make Perchlorate's. It will corrode if Chloride levels are let drop down too far in a Chlorate cell. It will also corrode if used in a Perchlorate cell that has a low Chlorate level in it. If using this anode material to make Perchlorate, start with a cell thas has zero (0.00%) Chloride in it and use Dichromate to protect the anode.
Pt has been plated onto valve metals (Ti, Ta, Hf, Nb) for use in Industry. If purchasing a plated Valve metal anode be aware of the coating thickness as some are very thin. Pt depths of 1.27 to 2.54 micron have been reported for Chlorine production anodes with wear rates of 0.5 grams per ton Chlorine (Metals Handbook).
Pt/Ir alloys have been used where current density's as high as 750mA per square cm were used. It is not too temperature sensitive as far as corrosion is concerned, keep below 40C. Current densities can be high at 300mA and up, 600mA has been use in a commercial cell for Perchlorate.
Wear rates of 500 to 220mg/Tonne have been stated. Smooth Pt, for example wire, (same as electro deposited Pt) is preferred as its wear rate is less that other forms of Pt, like for example thermally deposited coatings.
Pool Chlorination anodes are sometimes Pt based (as opposed to MMO).
MMO (Mixed Metal Oxide (Trade Name: DSA (Dimensionally Stable Anode)), usually made from the Oxides of Noble Metals, Ru and Ir, on a Titanium (a Valve metal) substrate. Used by ALL Chlorate Industrial setup's nowadays. Not recommended to be used in electrolytes where the Chloride level has been let drop very low (<30g/l). They can be used at relatively high current densities, 300mA per square cm, around 200mA per square cm could be considered a working value. There are a huge amount of MMO Anodes on the market. The corrosion prevention industries use them where they are used in very low Chloride situations at low current density. They are also used in swimming pool Chlorination systems.
MMO will not make Perchlorate AFAIK though some types may be capable of making Perchlorate.
MMO should not be operated at high temperatures. Pool Chlorination Anodes are mostly MMO Anodes though sometimes they are Pt based. Do not use Fluoride additive with MMO.

Magnetite It has been used to make Chlorates in Japan (and India) up to (and beyond?) 1971. It will make Perchlorate. They last a long time in a Chlorate cell even if there are low Chloride concentrations. Current density's up to 30mA per square cm have been used in Industry. Current density is not limited by erosion concerns but rather by economic reasons. Current efficiency suffers a lot. High temperatures do not erode them, up to 70C. They will not lower Chloride concentration to low levels possibly because of their surface electro chemistry.
You must use pH control in order to obtain Chlorate. Magnetite will make Perchlorate.
Ferrite's, as used in high frequency transformers and radio aerials, will not make Chlorate as they are not conductive.
Manganese Dioxide (MnO2) This Anode will make Chlorates very successfully. In a Perchlorate cell it erodes. This Anode is easy to make and has been shown to work in a Chlorate cell for weeks. Use at approx. 50mA per square cm. pH control would probably help greatly by lowering erosion.
Spinal Cobalt Oxide (Co3O4) This anode will make Chlorates and Perchlorates but it will not stand up to Chlorate cells for more than a few days. It only lasts for hours in a Perchlorate cell.
Semiconductor AnodesThis type of Anode is mainly concerned with Antimony Doped Tin Oxide (ATO). It is not a very successful Chlorate or Perchlorate anode. Tin Oxide doped with Bi Oxide is stated to be useful for Perchlorate production.
Diamond The Diamond Anode will make Chlorates. Perchlorates?
Titanium, Gold, Tungsten, Tantalum etc Theses metals will not make Chlorate or Perchlorate.
Lead Lead will make Chlorate and Perchlorate as (badly adhering) Lead Dioxide forms on its surface. Be prepared for a toxic mess as the Anode will corrode from the beginning.
Car battery plates have been suggested as Anodes for cells 1001 times. I have not read any reports of success using them. They will fall apart or passivate soon after going to work. The Lead Dioxide in held in a Lead metal mesh. It is not hard and compact like a proper LD anode. The Lead mesh is also exposed and will erode.

The Graphite Anode
The Lead Dioxide (Pb02) Anode
The Mixed Metal Oxide (MMO) Anode
The Platinum Anode
The Magnetite (Fe3O4) Anode
The Mn Dioxide (MnO2) Anode
The Co Oxide (Co304) Anode
The Semiconductor Anode
The Diamond Anode