I accidentally set a custom map marker and I can't figure out how to delete it. Not a huge issue, but it would be nice to get rid of it if I could.

Click on the map (not on the previous marker) as if you are about to set a marker and it will give you the option to remove.

Click somewhere else in the map, you should get a dialog box asking what you want to do with the marker....

Thank you! No more annoying blue map marker.

No, actually it just lets me move the marker to the new place, or fast travel or not. I remember being able to remove it under the original game and was wondering if the 1.2 patch
messed this up?

For that matter, I would LOVE to be able to place markers at other than designated spots: up near the Tower stone I found a shrine to Talos that gives 7 hours of immediate shout
recovery and want to be able to refresh this as needed.

Unless it's different from game to game, there's another one right outside Thieve's Guild.

There's an easy to find Talos shrine right outside Windhelm, across the bridge and up a small mountainside.

Not the patch, it's still working like "normal" in my game. Click somewhere to set, click somewhere else, get the option to remove it....

There's also a shrine of Talos in Whiterun near the Jorrvaskr where that worshipper is shouting about the greatness of Talos.

THAT voice actor certainly earned his pay: I've never heard the guy quiet yet :>

Don't click on a place. Click on an unmarked area on the map.

I know what he means, the marker sometimes will not give you the option to remove then it pops up when you don't expect it. It's a little frustrating but nonetheless a small bug. Thankfully I have'nt experienced the same glitches as other people so I'll live with it.