Swarmkeeper
Hero
I played in a campaign where a 1st-level character joined a party of 4th-ish level, and he got insta-killed by the first trap (which the DM didn't intend to be an insta-kill trap). I have to believe that's even more possible with five or more levels' difference. Does that count?
Yep - that can happen but I think that's more of a feature than a bug. DMs can over (or under) estimate the encounters they create. Hope the player hadn't already bought the mini!
The chance that a PC might die, especially a low level one, should be a part of the game, IMO. That's true whether or not they are in the midst of higher level party members. Encounters need not scale to the level of the party, either. Sometimes encounters should be avoided altogether. Sometimes encounters are cakewalks. Sometimes encounters are juuuuust right. But I think I'm veering a bit off the point here...
Are there other "serious problems" you had in mind when a lower level character joins a higher level group?