Why does this go wrong and in what situation?

Somebody mentioned it elsewhere, but it is a security risk: if you end up in a directory that's not under your control, and you do a "ls", it might execute "./ls" instead of /usr/bin/ls, and that can be doing anything, including piping your ~/.ssh/id_* to a remote server.

This can also happen by downloading something off the internet (git clone, or tar xz foo.tar.gz), or on a multi-user system (eg. someone can put any of these common commands into /tmp/ and wait for you to drop into it and try a "ls" there) — if you have any untrusted content anywhere, you are exposed.

A trip down the recursion hole. Also, scripts will inherit the relative path so they will have different absolute paths from each other. Seems easier to just type ./ so it's kinda funny in a "UNIX haters handbook" kind of way, but it's not even a fault in linux's command interface in that case. We've all been there.

Oh, that's without even going into the security risks and loss of portability.

Presumably a script that aliases a common thing or something and then it uses the same. E.g. someone adds ./sed that has some default params and calls sed. You’re intended to call it with ~/not-in-path/defaulted/sed and it is supposed to then call sed but instead calls itself if it’s earlier in the path hierarchy.

Might even be as simple as “detect if I’m running gnu sed or bsd sed and use the appropriate one”. Obviously you can not have this problem by being smart about other things but defense in depth right?