The second most common problem I have is finding a user, even if I know their handle. It was hard to believe how difficult that was the first time I tried it (admittedly, vanity URLs have made this easier).
1. See tweet in timeline, click the "expand" link in the lower left, or just some other blank spot in the tweet. 2. Hunt around until I see the non-obvious de-emphasized "details" link in light grey next to the date. 3. Click the "details" link and load the full page for the tweet. 4. Copy the link from the browser URL bar.
I don't know why they make it so hard and require me to load a whole other page and interrupt my timeline browsing flow. Annoyingly there's a "more" link on each tweet which I always end up checking anyway, and it doesn't have an option to copy a link to the tweet! You can "share via email" or "embed tweet" but neither of those gives you a useful URL you can just paste somewhere. The UI is a train wreck.
For example the fact that if you start a tweet with @ it will not show up on your feed. Stuff like that.
Search icon
Paste in handle, "@accountname"
Receive list of people mentioning @accountname
Click on one of them to view the account
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.