What are the effects of core shots and redrilling of skis?

Probably sounds like a silly question to most of you, but I'm in the market for a set of used skis and would like to know how these things will affect the skis. I've seen posts where people say that redrilling once is ok, but more than once is not. Do core shots, redrilling affect the performance of the ski, or does it just weaken the ski and shorten the life? Would a core shot repaired by an expert be much different than somebody doing it themselves and can you tell how bad it is by a picture? TIA.

Hard to say.  I'd start to be at least a little concerned about skis that had been redrilled more than once, but only because, like you, I've seen that recommendation elsewhere.  Obviously it's going to weaken the ski at least a little, but I haven't seen any hard evidence that it will drastically affect their performance or longevity.

I wouldn't be worried about small amounts of base damage.  If they tore a giant, gaping hole in the bottom of the ski... I'd probably pass, even if it was 'expertly' repaired.  You can fix the PTEX base, but if the interior layers were damaged, that's permanent.  And severe damage near the sidewall could potentially cause the edge to fail, which would be... bad if you were on the skis at the time.

Core shots: Coreshots happen... but need to be promptly repaired when they do. If water gets inside the ski and then refeezes it can cause further delam and tear the ski apart. If you hit the ski hard enough to gouge out huge amount of PTex it is possible the core was also damaged in someway.

Duplicate mounts: A problem if you want to mount your bindings and the holes are too close / block where you need the screws to go... eventually if you dril too much the skis are weakened and can be damaged. More holes also provides areas for water to get in.

Core shots along an edge are worse than core shots in the middle of the base. 

Re-drilling a ski for a smaller boot is worse than re-drilling a ski for a bigger BSL.  Properly filled holes under the boot are less likely to snap a ski than properly filled holes between the boot and the tip or tail of the ski.

IMHO, as one that has mounted thousands and repaired hundreds of skis, as in most cases, it depends.......
I've seen few skis break due to multiple drillings(four or more is excessive )but I have seen as many break with one improper drilling as well as,an improper landing, following "air"( for whatever reason.) In the old days, Spademans on Hexcels or The Ski were notorious for this.

I have seen skis with an improper first mounting have screws pullout. When following previous mountings, screws must not be too close to previous holes; if necessary, helicoils(ski-certs) can be inserted to provide greater retention. You can also pick a binding that has holes that provide greater distance from existing holes.
I personally have seen no correlation to BSL other than most "big/heavy" skiers, have a longer BSL, while smaller skiers are more likely to have a shorter BSL. (Although, this doesn't mean there isn't one.)
Core shots: as long as the core is not "broken" to the point of losing structural integrity and is properly dried prior to repair, it will usually function just fine. Any loads(unless directly smacking a rock, etc.,)will be spread over an area of the base(length/width) of the ski that provides a much larger area receiving the pressure, than the damaged area. No, they will not be as good as new but will still perform just fine. I have seen skis used extensively following some pretty poor repairs.
Most skiers would be better served to worry about keeping their skis tuned and waxed frequently, than the viability of a proper core-shot repair.
Even severe edge damage, although not good, can function as an outside edge when properly repaired. If you are buying such skis, keep in mind what the price is.
Obviously, ski racing would require the ultimate in performance, therefore, high quality repair is critical.