I've only travelled twice where multi PNRs were a factor but seem to have had a minor and a medium glitch as a consequence.
The minor one was coming back from LAX-AUS-LHR/LGW-DUB where at LAX we spent at least 20mins going between bag check, ticketing desk, supervisors etc just to get bag checked/BPs for LAX-AUS (on a BA codeshare) and AUS-LHR (on an AA codeshare but different PNR). At 0500 the LAX staff were a little grumpy and weren't listening to me trying to say that we have one ticket but 2 PNRs but with persistence we got there in the end.
The first time on an ex-EU TP run to HNL I couldn't check in online with BA for the first sector - perhaps because I'd tried with at least 2 of the PNRs that appeared - so did so at the airport. The nice lady at BRU seemed to have no problems, checked me in for BRU-LHR and said I'd have to check in again at LCY. Fine....if you say so. When I arrived at City and presented myself at check in they denied all knowledge of me and sent me to the ticket desk where they said, after a 'sorry you have no res in the system' funny five minutes, that they could see that I once had a reservation but I should call AA (with whom I booked) to resolve it. I said something about 'Oneworld?' and one of them took pity and called AA, which resulted in 15 mins getting nowhere so in the end they just put me back on the flight (I don't know how). Coming home from HNL a similar thing happened, I think checking in for the first US sector appeared to remove the AA codeshare JFK-LCY one, but I called AA and they resolved it without any fuss.
The moral of the story being that one ticket and multi-PNRs obviously has some potential traps, in my case if checked in for the first sector on one PNR yet that sector appears in another, the other PNR will think you did not travel and thus remove all the booking. Or that's what it looked like.
Maybe it's only ever happened to me and in any case someone else can probably explain how to avoid problems like this.
Awareness that this could happen is probably better than surprises!