What are some common mistakes students make with acids and bases?
Splashing them on their clothes....
Splash a bit of dilute acid on you clothes, the next time you wash that item, the acid (or base) has weakened the fibre of the cloth, and you get a hole in your favourite shirt or jeans (as an undergrad I had a couple of colleagues who exploited this phenomenon to produce ragged and holey jeans..one of them is now a big noise executive in the clothing caper!)
I acknowledge that this is not what you want to know, but perhaps you could try to narrow down the terms of the question. When you work with acids and bases the BIGGEST mistake you could make is NOT to wear safety spectacles and a lab-coat!