Beware spoilers:

Fought a couple of very hard to kill Spectres in Wintersun but didn't receive any xp for them. Is this WAI or a bug?

Working as intended.

In fact it is the same specter over and over again and he will usually keep haunting you for you stole his whip from his grave.

If you manage the difficulty check on knowledge you can understand him complaining for stealing his whip and demands it returned.

Ah I see. Thanks.