Hi J.!
I have a 21 month old and she started day care at 6 months and I didnt have this problem! I know my friend, her little girl is 7 months older than mine and the first day care she went to, her daughter used to come home w/ food all over her. Long story short, she ended up moving her to a different day care. It wasnt just the food thing, there were other things too but this alarmed her, too. The other day care she went to and continues to attend, she didnt have this problem.
I can see that accidents happen but your right, why not use a bib or change him/her when something gets on them? I think these are potential signs and you should keep a close eye on things and yes, I would say something about it, in a nice way and see how they react!
My BEST advice to you is to listed to your mommy gut! I listend to mine and I am so glad I did and didnt think I was just being a first time mom!
Good luck!
K.