That plot sounds like something that Adam Sandler would shit out these days, possibly with him playing about 50 of the children himself. Thankfully Delivery Man feels more indie* than zany. At times writer/director Ken Scott does force his message down our throat a little (at one point VV discovers that three of his kids are in order: black, gay and finally disabled.), but he mostly keeps Delivery Man just about the right side of sentimental. Obviously with someone like Vince Vaughn a lot of the enjoyment you get out of his work depends on how much you like him as a man (as he basically just plays Vince Vaughn in every film). Personally I really like the big guy so I tend to enjoy most of his stuff and there is a lot of laughs along the way in Delivery Man (mostly in the interchanges between Vaughn and Parks and Recreation‘s Chris Pratt). There is nothing to separate this movie from many others like it but if you are looking for a nice easy watch this fits the bill.
*This is probably because this film has already been released as an indie film by the same director as Starbuck. As I haven’t seen the original I have forgone any kind of comparison.