The first thing thats really interesting in this thread is how much crit you have received, lots of it very useful but it's interesting how much of it you have compared with other photos you've posted. Because the thread title says first paid work - people have decided to be more frank and respond more than your normal shots.
My advice to you is to selectively listen to the crit, everyone has their opinion of course but doesn't mean they are right or wrong, I'd be valuing the opinions of the people who have critiqued whose work you admire. Not everyone's thoughts are as valid as others if you know what I mean, including my own
1. I agree with the dof thing others mentioned, but your background and the expression on the babies face is excellent. I also love the light in the background falling on the trees. If mum had been smiling and leaning her head onto the baby I think this shot would have been perfect.
2. You could probably fix the housing estate bit from this shot with some clever cloning and a bit of a crop. I think the babies expression and the colour in her eyes is worth keeping and fixing the background - again I love the light falling behind. I would imagine this shot shows the personality of this little un to the parents. The leaves to the right? clone them out easily, also looks like a bit of lens flare bottom left which you could fix.
3. I like this one a lot, I think the dof effect works well. Others disagree but opinions differ. Love the expression on the first girls face and he bokeh is really dreamy. The fence is fine in my opinion, if it wasn't there by the looks of the exposure you'd have a a white mess of a background of blown highlights.
4. This one is lovely too. Agree with the comment about the clipping of the foot and knee though - if this is a crop you can fix that though. Again, I don't have a problem with the background.
5. Love this one, great expressions, sharp focus and good background and bokeh. Top shot
6. Really like this one too. It is almost impossible to get that many people smiling at the right time when the little boy does, having tried this many times with my 14 month old I know how hard that is. My advice would be to put your camera on a tripod, use a remote release and have some toys, balloons, bubbles jumping around and laughing whatever it takes to get that kid to look and smile and you'd have nailed this one. I don't think you have to have their feet in it, you've cropped it high enough for this to be deliberate
7. same as above - tough job getting the baby to smile - she may not even smile yet? tripod and toys etc. God background and great focus and exposure
8. This is kind of the pose i meant for one but because baby isn't looking and her right hand side is cut off I don't think this one is great.
9. Love this one.
10. The wide angle thing definitely ruined this one, and look the baby is looking right down the barrell!! should have gone with more dof and this could have been a winner - looks like you went higher to avoid the distractions in the background which was a good choice
11. I think we either need to see more of mums face and body or none of it - could have been a nice dad shot.
12. This is superb and my fav of the lot. Love the expressions and the way the family are all interacting. very natural.
As for the comments on these being good instead of great or not pro standard, pretty sure you aren't claiming they are pro standard. And I would imagine the customer does think they are great and has been wowed by them. If they were then job done