Firstly would like to say that overall I loved the game and hope there's many more to come, I loved the humour, with some laugh out loud moments, the little references (Futurama, Sam & Max, etc.) and the tone is nice and eerie at times.
However, here are a couple of things I feel need to be improved upon for any future releases:
1) Uneven difficulty curve:
Is it just me or does the game seem to have a difficulty curve more along the lines of a sine wave than any actual progressive curve. The game seems to randomly alternate between difficult and easy puzzles, especially in the latter segments, the difficulty should definitely be more continuous, escalating to the point that the latter half of puzzles should take all the puzzling skills you've learned previously to solve. I know Puzzle Agent tries to do this already, but in doing so it throws some very easy ones at you (the last jigsaw? so easy!).
2) Puzzles that solve themselves:
a) The jigsaw-type puzzles are RIDICULOUSLY easy, essentially solving themselves. I'm almost certain one could close their eyes and just move bits around and eventually solve the whole thing. The biggest reason for this is the *very* generous "snapping" that occurs. I'm all for snapping (happens in games such as Professor Layton), but it should require your placement be a LOT closer than it currently is (maybe within a couple of pixels, no more).
b) The tile rotation puzzles are also very easy, primarily because each tile tends to lack any ambiguity as to its orientation and it's also easy to see what the "expected" orientation is due to very visible seams on each tile that only really match up with the correct partner.
c) The birds carrying bags puzzles were pretty easy too because of the "no crossing lines" rule. That immediately makes it *very* difficult to attach the birds to anything but the bags directly beneath them, making it much of a no-brainer.
3) Puzzles where the rules aren't properly explained.
I can only think of one instance (navigating the brain) where I wasn't aware of the rules of the puzzle that resulted in what I thought was a success being a failure (namely that you MUST have an arrow in each available space - I merely thought a signal travelling in a straight line only needed an arrow when you wished to change its direction).
4) Hints that don't help and How?'s that don't explain the puzzle:
There were one or two instances where I was forced to use hints because of a sudden escalation in difficulty, but when I did I found the last hint was still kinda ambiguous, either by not explaining enough or not providing enough of a visual input as to how the puzzle was supposed to behave.
However, a bigger deal for me was using the "How?" button after solving as a puzzle, since I like knowing if the way I was thinking about the puzzle was correct or not. In quite a few cases the How? page would have a single sentence saying nothing really about the process of the puzzle itself, the optimal way in which to solve the puzzle or explain only the first step in a multi-step puzzle, so it was a bit disappointing.
I couldn't help but laugh at the deceptive 2nd level hint for the birds in a row puzzle.
5) Lack of puzzle diversity:
Title pretty much says it all, could have done with some more puzzles, some more negative space puzzles (since you threw one in right at the beginning!), maybe some "spot the difference" puzzles, crosswords, number problems, etc. I understand you're trying to hit a certain demographic here (Professor Layton Lite!), but I would have preferred something a bit more Laytonesque.
6) Not many puzzles:
Outside of the main plot there's not much in the way of puzzles, maybe 8 or 9 more, most of which are just different variations of the same (3 birds with bags, 3 bugs in boxes, 2 football passes and maybe 1 or 2 other unique ones). I would have been happy if these didn't even exist, but were instead replaced with 9 or 10 more unique plot-related puzzles.