Those metal clips on the side of the ceramic part are supposed to catch the edges of the reflector. They may need to be bent a little to get them to securely hold the lamp holder. Discolored wiring isn't too uncommon (or unsafe), if it's really charred it will need to be replaced.

Thanks, The clips are too short to reach the sides and still be stable. I did notice a slot in the side of the can. I guess I will make sure they put a socket that mounts to the side.

On that style of fixture the lamp clips into the trim. This is normal.

I was checking other fixtures that have the same type of socket and this one is still working but the white wire is discolored and the black looks melted. Should I be worried about this or the whole lighting job?
Out of the 20 or so fixtures only 3 where installed with this free hanging socket (the clips on the side are too short to clip on on anything at the right height)

Here is a link that might be useful: {{!gwi}}

what size bulb do you have in there versus the rating of the fixture?

The Bulb is a 50W PAR20. The writing on the inside of the can says Max 50W PAR20/R20