Mistake of fact is a situation which you may have in fact broken the law, but due to extraneous circumstances you aren't held legally accountable. Sometimes though you still have to defend yourself in spite of not actually being liable to the crime.

How can you use a mistake of fact defense with traffic tickets?

You have to prove that there were circumstances beyond your control when getting your traffic ticket.

For speeding tickets one of the most common ways this can be used is because the speed limit sign is somehow blocked or gone. After severe storms a branch might cover the sign or it's completely fallen over. In this case you aren't trying to speed or do anything wrong. It's a good idea as soon as possible to go back to where the speed limit sign is gone or blocked and try to take photos to defend yourself.

This also happens with tickets where you have failed to stop. For example a stop sign might not be there or the lines on the road are faded. Photo evidence will work the best when bringing this up to the judge.

For the most part judges should be understanding in cases where there are circumstances like these. You have to be careful that you don't actually admit to the judge that you were breaking the speed limit as posted. Instead make the case that the city didn't fulfill it's responsibility to you as a driver.

In vary rare cases this defense can be used when speed limit signs are changed and you happen to one that's pulled over that day. This isn't a completely strong defense but it's an option that you can use.