Would a small deviation in an experiment mean that something is wrong with the experiment?

Not necessarily. It might mean that the experiment has a highly stable outcome. You need to evaluate if that is true or if the experiment is flawed. It comes down to theoretical expectations versus experimental outcomes - you should know a priori (before the fact) what to expect, so you can know if the results are good.

For instance...

If you were measuring the radioactivity of a sample with a relatively low count rate using a detector that recorded counts in each second, you would expect a poissen distribution.

If you were measuring the same sample with a detector that counted for 1 minute, you would expect a more gaussian distribution.

If, on the other hand, you were measuring the wavelength of a red laser, you would expect that every single observation would give you the same results, within an extremely tight distribution.