In the movie Inception, why does Cobb's passport not get stamped properly?

First of all, please note that this answer is not based on facts and is just my personal observation.

As you have said in a comment, Christopher Nolan is too great a director to allow minor flaws as this in his movies. (And I guess it would have been easier to stamp a real seal on the passport than one without a date).

Inception is almost completely based on dreams within dreams and in different times. So if a specific date has been stamped on Cobb's passport, it would have given definitive evidence on the exact date and reality Cobb was currently in. And it would have more or less succeeded in lowering the confusion level of the audience.

So my conclusion is that this was intentionally done so as to leave the audience further in the dark as this also is very unreal-looking (to have your passport stamped without a date) and confusing about the "real" reality.