I'm a newbie, so this probably isn't anything you don't know, but just in case...
1) I had a wrestler whom I switched to training with a crossbow, but he wouldn't pick up any bolts. He kept sparring in the barracks, bashing people with his crossbow, instead of shooting at a target. Yes, he had a quiver, but it stayed empty.
I tried a lot of different things before I noticed that he was wearing one waterskin and carrying another in his left hand. In his right hand, he was holding BOTH his crossbow and his shield. So I set the second waterskin to dump and (if I remember correctly) also told him to stop carrying water. That did the trick. Once he got rid of the second waterskin, he was able to pick up bolts and start shooting.
2) I switched another wrestler to hammerdwarf, but when he went to pick up his new equipment, he just stopped in the middle of the hallway and seemed to be stuck there. I had a silver hammer available in the next storeroom, too.
Again, I tried many things before noticing that he was wearing leather, when I'd (long before this) set him to wear chainmail. I checked the Stocks screen, and I seemed to have enough chainmail. But when I zoomed to them, I discovered one dwarf wearing plate mail (as instructed) AND the extra chainmail.
Apparently, the fact that his chainmail was already in use was enough to lock up my prospective hammerdwarf. For some reason, this hadn't been a problem until I'd switched his weapon. I don't know why. But when I switched him back to leather, that did the trick. He instantly went to the storeroom to pick up his hammer. No more problems.
Note that it's kind of weird that dwarves can wear multiple suits of armor. And it makes it VERY difficult to tell how many you've got available for other soldiers.
But I was happy enough to figure out these two problems (eventually!), without needing to make a fool of my self here.
Bill