Use your boys as a "gateway" to help dad. :) For example, when dad gets home in the evening..."hey everyone, let's ALL hang our coats up and put shoes away!" Or, "Boys, Dad is going to hang up his coat, why don't you hang yours up too?"
My husband is a slob, too, but mostly because he gets easily distracted and he's not that concerned about the mess. I just let him know that it's important to me that our daughter learns to put her own stuff away, and that it would be really helpful if he could set a good example.
So, instead of him (or you!) putting your kids toys away, have them do it. Teach them (and him!) the importance of "everything has a place." I really think that my husband is "learning" to be neater because I have him work on it with our daughter (even though he still has to ask me sometimes where things go). Use labels if you have to!
Also, the rule in our house is "one person cooks, the other person cleans" (and stacking dishes in the sink is not "cleaning").
Oh, and just tackle one thing at a time. You don't want him to think it's "too much" and give up. Similarly, let him know how much you appreciate him taking the effort to do XYZ.