when a venue is booked for a date, and the date is on the signed contract, but the venue wrote the wrong day of the week (like Saturday vs. Friday) ??

I would think that the date would be controlling and you should have a good claim against them for any damages you incur as a result of their breach of the contract.  However, it's possible that it would be considered a mutual mistake of fact, in which case they may be able to wiggle out of it.  It's an interesting issue and may require additional legal research to see if any courts have addressed this before.