The offset will be most extreme at extremely close range, but because the laser can only be zeroed at one spot in the bullet's trajectory there will be offset issues at every range except the range at which you choose to zero your laser.
Generally once you get out past 5 yards the offset is minimal out to well beyond handgun distances, but if you are trying to make an extremely precise shot you still need to know the offset.
For most people the offset is well within the margin of error inherently present in their shooting, but it's still worthwhile to understand your setup and how it works. Use a rest if possible to remove shooter issues from the equation as much as possible.
So at what range should you zero your laser? It depends on personal preference.
From the factory the CT grips are supposedly zeroed at 50 feet. Some advocate making your zero at precisely 15 yards, others at 25 yards, and others at 7 yards.
It all depends on what you are comfortable with and what works best for you. The most important thing is to learn how your setup works and to train with it.
Another common failing people have when using a laser is trying to make the laser absolutely still. This is never going to happen.
What you must learn to do is to work within the acceptable "wobble zone" of the laser, essentially learning to keep its movement within the acceptable hit area you are working with.
The tendency to try and get the laser still and then hurry the shot right as the dot stops is what typically leads to people snatching the unholy hell out of the trigger.
You need to be able to make a good trigger pull even while the sights/laser are moving around while you simply keep the sights/laser within the A zone to make the necessary shot.
You also need to realize that lasers are a target indicator. That bright red dot shining out in the night can give away your position or telegraph your movement.
This is why the Crimson Trace grips are preferred as a laser solution. They are activated by a pressure switch rather than a traditional on/off switch allowing you to quickly engage the laser when you have to shoot and to leave the laser off when you don't need to shoot. If your weapon isn't lined up on a threat, your laser shouldn't be on.
Moisture can affect lasers dramatically. If you get a drop of water on the laser diode it can completely block the laser or can cause the laser to spider web or take on odd shapes at longer ranges, reducing the laser's useful range and precision.
You should make a practice of checking your laser for function and making sure the dot is appearing properly as part of your every-time-you-walk-out-the-door equipment check.