This is a really broad sweeping generalization, but I think single moms that are dating are naturally more cautious and protective of their kids than many single dads would be. A mom may always worry (at least initially) about a man's intentions, especially when there is children involved. I know as the mom of a 4 year old daughter, I certainly would be. A dad probably just assumes that his lady friend will be fine around his kids. Remember too that a kid saying he wants his dad's friend to stay for a "sleepover" doesn't mean the same thing to a kid as it would mean to an adult. He's probably thinking it's like a party with eating popcorn and ice cream and watching movies and then having pancakes in the morning.
My husband had been married before and his sons were 5 and 6 when we met and started dating. He almost wanted to introduce me to them right away, probably because he was really serious about his feelings for me and was already thinking of me as potential marriage material. I did meet them for the first time after only a few weeks - we went to a carnival all together and had a great time. He had not introduced any other women he had dated previously to them before that. I know for many people that might seem way too soon, but it still worked out. We got married 4 years after we met and it will be 8 years this June. Their mom on the other hand had her first loser boyfriend move in with them after only a couple of months and all we heard about was how he was going to be their new daddy, they were going to have a baby, etc. - it was probably pretty confusing for them and fortunately it didn't last.
You are entitled to your opinion, but you can also try to trust your friend to be able to make sound decisions for herself. I think it's too soon to judge either way and only time will tell. I would probably only say something if you start noticing other things that get you concerned.
ETA - @Dad on Purpose - Is it really immoral to get divorced? IT HAPPENS! Who is to say he is the one who wanted out? How is it that he runs from relationships at the drop of a hat? Where did you get that from in this post? My husband did not want out of his first marriage - his ex-wife did. But then would that mean there was something wrong with him for her to not want to be married any longer to him? Being divorced doesn't make you "damaged goods!" How is him wanting to introduce his kids to her a reason to call CPS?