Is it possible to learn all skills in Glitch? I haven't seen anything definitive either way, but it looks like you can.
Yes, it is currently possible to learn every skill available, and many people have. The only disadvantage to learning more skills is that there is a compounding 3% time penalty for every skill you learn above a certain limit. The limit is determined by your current level of the Better Learning Skill.
The effect of this is that learning many 'fast' skills will make the longer skills later in the tree far more difficult to learn. The current maximum penalty is over 4x the base learning time, so for skills that take days or weeks, this can be significant.
Thus, learning some skills you aren't interested now might penalize you in the future, should there be a long learning time skill that is introduced into the game later down the line. The game developers have said that they have many skills planned for release in the near future.
One of these skills is thought to be Unlearning, which will allow you to 'forget' skills that you don't have any interest in retaining. It would take a fraction of the time it takes to learn a skill in order to Unlearn it. The time taken to Unlearn a skill is not affected by the aforementioned penalty and the Unlearning skills themselves also do not add to the penalty.
The Skillifier is a tool I developed to track skill times and help you prioritize, if learning time is an interest/concern: