My MIL is a very finicky person and she likes to keep things in order in her own home. But as soon as she comes over to our place, no matter how clean it is, she manages to find fault! How do I tell her, she needs to STOP, without sounding rude or crazy!

Sounds tricky. Could you ask your husband to help clarify what exactly is bothering her? Otherwise, how about bringing her out more often so that she will not be in the house to fuss over the way things are? It could be that she is simply bored. Ask if there is any classes that she is keen on and sign her up for it? Not sure if these will help but hope it gives your some inspiration... Take care!