This corner of the shower seems to be having some mold issues from regular use. Water seems to be collecting in that spot after a shower and doesn't seem to be draining properly. Is there anything I can do for a permanent fix?
I've tried keeping my bath fan on for an hour after the shower and don't want to have to squeegy it after each use.
Those tiles should be slightly sloped towards the drain, I am guessing they aren't or aren't enough so water just sits where it lay.
Squeegee is the cheapest and best option, you should already be using the squeegee on the glass after use anyways, but ain't no body got time for that.
If you are leaving the shower door open when you are trying to dry it out with the exhaust fan; a larger or additional exhaust fan or a dedicated dehumidifier are reasonably easy and cheap options that may do the trick. Personally, I'd rather add another fan than the hassle of a dehumidifier.
Removing and resetting the tiles with a properly done slope and corner is the best option, but you may be in for rebuilding the entire shower because of the risk of compromising the waterproofing during demo if the waterproofing is membrane.