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Although ASTM specifications for Diesel Fuel are a number of pages long, only 3 or 4 things are technically required for proper operation. The rest of the specifications are politically motivated, generally to protect someone with a financial interest in the rule.
The important things for diesel fuel are:
Clean
Dry
Ignitable
Other good qualities are
Lubricity
Low temperature flowability
Luckily, all of these properties are easily attainable with waste oil.
Waste Oil Cleanliness
Relative to waste vegetable oil, motor oil is fairly clean. WVO may have fish parts, batter, salt, corn meal, water or any number of large debris. Engine oil filters are generally around 20 micron, so the oil that comes out of an engine is relatively clean in comparison.

The only way to get oil properly cleaned for LONG TERM RUNNING without problems is a centrifuge. The idea is simple, things heavier than oil will come out, and since most of the problem causing things IN your oil are heavier than oil they WILL come out if properly centrifuged. However, many are present at the molecular level making them impossible to remove by just filtering. A strong centrifuge is required.