I'm buying an REO property. The bank decides who will be the title company. I've read online that the title companies used by the banks sometimes make mistakes and don't do a thorough job. Is there merit in hiring my own title company to do a search? Would that be an unusual practice?

You could do that but I wouldn't bother. As long as you buy their title company's policy you're covered. If they make a mistake then they have to fix it.

If it would make you feel more comfortable you could always hire your own title company to do a search, compare it to the bank's search and then just pay for your search but not buy the policy from your company, and buy the policy from the bank's title company instead.

Yes, it would be unusual. Title searches are not rocket science. Yes, people can make mistakes, but that's why you buy title insurance - just in case.