Safety-wise I presume you're relatively low risk? There is alas plenty of scope for quality issues though...
A few thoughts from experiences with a few contract soft drinks packers:
1) For anything QC related, it's worth clarifying if what they are showing you is actually the case for all raw materials/finished product - lost count of the number of times I've seen brand owners expecting x/y/z to be tested, and packers not testing anything. Some of them can offer quite comprehensive QC services, but only do so if they've been told that you want it and you're prepared to pay for it
2) I'd look long and hard at raw material intake and production preparation. Again I've seen unfortunate incidents at more than one site, where a raw material has arrived and it's been used without checking, because "the client sent it so it must be right". Alas the client may have sent something, but if the pallets have accidentally been switched at the depot and no-one actually reads the labels or does any testing on the raw material then apparently there are contract packers who will use completely the wrong raw material without noticing until the product is part way through being bottled, at which point someone is surprised that the Brix value is rather different to the expected tolerance...
3) If there is any storage, particularly of open/part packs of raw materials, then I'd examine how this is managed. Again I've seen more cases of "we didn't know it was supposed to be frozen after opening" and "we didn't know it should be used within three days of opening" than I'd like to admit. Key points to look for are whether there is a formal process to manage the collation of this data, and how it is communicated and used (and whether it's actually working in practice).
4) Is there a system for holding approved product reference samples for taste panelling against new production? And is it actually used and working?
Again I'd want to see some evidence of this. Not necessarily a widespread issue, but a few times I've seen very obviously different batches being shipped that should readily have been picked up by the taste panel the packer claimed to have done.
FWIW I've also seen some very capable packers around Europe, and as a general observation there seems to be a not unsurprising correlation between cost and overall quality of service