There are so many amazing picture books out there aimed at this age group. It's hard to recommend just a few. You'd be better off visiting a library to let him explore for himself what he likes, then investing in any that are real hits to add to your own collection.
If he likes Time for Bed Little Dinosaur though there is a whole series based around different characters, same with There's a _ in your book.
Other series he will probably enjoy if he likes those are:-
Ten Little (Pirates, Dinosaurs, Robots, Superheroes etc)
The Dinosaur who pooped (a planet, a princess etc).
Aliens Love Underpants (and monsters, Dinosaurs, pirates etc)
Supertato series
Men Men is usually popular with 3 year olds (personally I much prefer the modern ones written by Adam Hargreaves, the originals by his father Roger are quite dated now but Adam Hargreaves is doing a great job of keeping the franchise alive by writing more modern stories with relevant themes).
Authors I would highly recommend for this age group:-
Julia Donaldson
Sue Hendra (author of Supertato series but loads of other amazing books perfect for this age)
Jill Murphy
Judith Kerr
Peter Bentley
Michael Rosen
Nick Butterworth (Percy the Park Keeper etc).
David McKee (Elmer etc)
Mike Inkpen (Kipper etc)
Tony Mitton
Giles Andreae (especially Giraffes Can't Dance)
Rachel Bright
Tom Percival
Jez Alborough
Honestly though, there are far too many amazing books aimed at this age group, that list is just scratching the surface. I'm sure to have missed so many.