In the Twitter OSX app, if I want to find an account, my method is:

  Search icon
  Paste in handle, "@accountname"
  Receive list of people mentioning @accountname
  Click on one of them to view the account

Pretty insane that it wouldn't just give me that account name first followed by similar account names.

Another classic thing is the autocomplete on account names when writing a tweet. It will show me (and prioritise!) accounts I've never heard of and more often than not the account I'm actually wanting is last in the list.