Also, immediately next to this closet is a small half bath.

Can you remove the closet so the wall is flush with the wall and railing above without impacting the bathroom? It's not possible to tell from the photo.

Yes it's flat and collecting dust..also I do believe it's possible to remove so the wall is flat. Any idea of how much it could be?

remove it

Just find someone capable of doing the whole job for an estimate...(to save money you may want to do the demolition and clean up yourself if there are no complications in construction)... this may only leave cost of sheetrock work and floor repair...definitely worth whatever it costs... as this will never look right as is

As Chip would say, "it's demo day."

I think someone was looking for extra closet space and added that closet there. Remove it.

Hm, I'd say this is a pretty easy DIY job -- check with a professional when you get that "estimate" but it can't possibly be load bearing so you should be safe whacking it away.

Once you remove it (don't worry about hurting anything!) have someone drywall the wall that butts up to the bathroom (that's not really a DIY job if you want it smooth) and then you could do a cool bench/open shelf concept for coats, shoes, etc. to tie the space into something usable vs. having it just open and sitting there as semi-unusable space.

Or, smack that thing out of there, do a DIY drywall job and get some cool textured paint-able wallpaper to cover imperfections and find a cool free-standing wardrobe to replace the closet for storage and create a 'feature hello' wall as you walk in. Good luck!

Any flooring issues to think about if it is removed..? Hopefully not, it needs to go.

mirrored doors?

Hummingalong2 -- very good point;

If the owner decided to create a 'focal' area, I think that would easily be handled either in that section, or preferably (in my opinion), extended to be the same as the doorway entry -- will make the space appear much larger and tie in well. Wherever they are, there are often 'designer' tile places that sell overstock or past season designer slate, tiles, etc. for about $1/square foot. A person might have to work for it, but would be well worth the effort.