S.K.
If there is anything we learn as parents, it is to always go with our gut. If you are uncomfortable in the slightest, that is ok. I agree with you that especially being the first day your child was there - whoever picked him up should have been asked for an ID.
Next, communication between teacher and parent is of the utmost importance. You do not see your child all day and you need to be made aware of his day. Especially in the beginning. He is still in transition and this is very new to him. The way his day is will set the tone for the rest of his evening. If he didn't have a nap - he may need to go to bed early. If he didn't eat lunch (or ate very little) he may need a larger dinner, or need to eat earlier than usual.
I think you have every right to go in there tomorrow and speak with the head of the school and also the teacher to make sure they know up front your expectations as his parent. If you are not upfront in the beginning, they may take advantage of that and feel like you don't expect what they are supposed to be doing in the first place - therefore won't follow through. They have your child's life in their hands and they need to respect you for trusting them with him.
It's ok that you have him in day care - every parent has a right to do with their child what they need. You know what is best for your child. No one can tell you what you're doing is right or wrong - just go with what you need to do.
And, if your Dad goes tomorrow and picks him up and they don't ask for his ID - he should consider telling them he expects to be asked for it every day until he is recognized - and he can ask the teacher for a written report of your sons day. That way they know he is also aware of your expectations.
I hope this helps. While I do not have a child in day care or a MDO program yet, my sister has shared many stories with me on situations they've encountered. I've found through her that the more open and upfront you are, the more serious they take you and know you are paying attention. I know that some of this seems easier said than done - I agree - but setting the standard for your child's care is what really matters.
Good luck,
S.
PS - Be sure to keep communication open with Karson as well. I know he's only 21 months, but he senses your sincerity and love when you talk about his day. When talking with him, stay positive and smile. :-)