So I'm looking at a Mauser police Luger with a police "sear safety" on it.  What is that, and is that desirable?  Thanks.

Common at least with police Luger's as they all had them from the Wiemar period through the fall of the 3rd Reich. Something rare to find on a police Luger would be a magazine safety as many that were originally fitted were later removed in the mid 30's.

What is it though? I'm just curious. Looking at a nice Mauser marked Luger with one on it.

Well a photo or at least a description would be handy. Is this a Banner Mauser marked, a 42, S/42 or byf marked luger?

Yes. Banner Luger.

Quite simply it is a piece of spring steel riveted on the frame that has a pin which blocks the sear bar from moving unless the trigger is pulled. On early Lugers the sear bar was partially exposed. Pressure on the sear could make it fire unintentionally. This was later alleviated by relieving the sear "cutting it back further" however it still could go off if something got under the side plate.

Here are pictures of my 1921 police DWM. The sear safety rivet is just below the DWM marking.



Here is a side view, you can see the semi exposed sear bar just protruding from the side plate.

Nice 1921 DWM! I have one also SN# 4199. My Dad brought it back from WW2
Nathanhale