Time stamp, when present, is always located in top/right corner of the screen when watching a multiplayer replay. It gives an exact time of things happened in it. Not to be mistaken with local time which can be displayed in the same place; check attachment so see what I mean by time stamp.

From what I could figure out is time gets stamped at the beginning of a qual/race. So, if a player connects to a server in the middle of either and saves a replay afterwards but before a new qual/race is started, replay will not have a time stamp. This kind of replay will only have current local time displayed which is meaningless.
When a player that records a replay is present in the server when a new qual/race start - time is stamped properly.

I'm under impression that this is bug and time should get stamped in both occasions. This bugged me for a long time as I thought my LFS is broken somehow but I finally found what causes it. Also, I don't know if it's worth mentioning but my own replay saving is set to manual (options - game).

All said was concerning MPR but for SPR is interesting too as time doesn't get stamped in either occasion which is strange. Would be cool to have time stamps there aswell.

I have been given that a thought aswell a few times, but I came to the conclusion that a your local time needs to change date (to the next day) before timestamp is shown.

EDIT: I'm just talking bs, don't listen to me :something ... you're right