Well your husbands a twat!
Of course there's mess! They haven't the motor skills for there not to be!
I've a fabulous photo of dd somewhere fallen asleep eating spag Bol where the spag basically looks like her hair and she has a "beard" of mince!
It's one of her dad and I's favourite memories of dd.
In spring/summer I used to strip her down for mealtimes! At least reduced the laundry! 
And a dust sheet under the high chair!
In response to his attitude I would definitely be making dinner times his Job! No way he'd manage any better! Dick!
I'm guessing at least part of the reason he split from his ex is because he did sod all parenting!
Mines 20 (yes years!) and STILL makes a mess eating certain dishes. 
Hell even I do! I was eating bagels earlier and got cream cheese on my cheek and nose! I'm 48! Frankly I can barely be trusted with things like spaghetti or wraps!
You need to address the constant comparison and criticism with him and basically tell him to fucking pack it in! If you're not bf I'd be tempted to head off to your mums for a day, leave before breakfast, and tell him you expect him to take full and proper care of baby AND keep the house clean and tidy and leave him to it! If he's a decent sort that won't neglect baby this could be a good way of getting it through his thick head that parenting isn't actually as easy as he seems to think!
Are you able to chat with his ex at all? I bet if you did you'd find out he's talking shite! My ex tried this a little with wife 2, where he came unstuck was she and I were friends prior to the affair so we actually felt quite comfortable chatting about the kids together and I was able to dismiss his claims that dd was an easy baby! (Far from it!) and that I was super mum!
He'd tried to use the fact I've a lot of baby and young child experience (ex nanny and childminder which wife 2 knew to be true) to make her feel inadequate while simultaneously being sod all use himself! He'd also manipulated her into thinking he "couldn't cope" with certain baby related tasks...
I soon put her straight that he was perfectly capable just didn't like doing them!
Don't let him manipulate you and tell him straight this is his baby too and he needs to step up!