For starters, the answer to the question as put is that yes, there will be crime. As many others have already said, there will always be crimes of passion because, well, in those cases, you aren't thinking about the consequences of your actions. That being said, there's a really strong temporary insanity defense in this case: "Your Honor, of course I was temporarily insane when I killed my wife! I'd have to be! If I weren't, I'd know that I'd get caught!" (though that's only relevant if there's a court system which cares about such distinctions).
Now, as to premeditated crime, there are a few variables which are currently left open which influence the possible answers. Most significant are the number of hindsight seers and the difficulty curve in looking further into the past. The number of seers is needed in a per-capita or per-crime basis. In your question, you state that it is harder to look further into the past, but it is unclear how the difficulty ramps up: can the average seer see one minute, one hour, one day, one week or one month into the past?
Looking at these two variables, we have four possible scenarios:
- Many Seers / Average can look > 1 day, week, month into the past
- Few Seers / Average can look > 1 day, week, month into the past
- Many Seers / Average can look < 1 hour into the past
- Few Seers / Average can look < 1 hour into the past
Obviously, the hindsight times given above are merely representative: seers can look reasonably far into the past, or not really.
Let's go through these scenarios briefly:
Many Seers / Average can look > 1 day, week, month into the past
In this case, there probably won't be much premeditated crime.
The reason for this is that if the seers can look that far back into the past, then I disagree with the vast majority of problems raised by other answers. Seers don't need to identify the perpetrator (whether or not they are wearing a mask), since they can just follow the perpetrator back in time to their home or forwards in time to their current position (if hindsight is fixed to the seer's current position, the seer can just go "ok, the perpetrator went around that corner", walk to the corner, activate hindsight once again, and repeat the process until they're at the criminal's doorstep). Kidnappings are also not an issue: start at the victim's last known location and trace their steps to the kidnapping and all the way to their present location.
The only such crimes would be committed either by untouchables (judge's son, as others have mentioned) or people who have really dedicated themselves to pull it off: moved out of their house into a hotel with a fake name and lived there for 2 days/weeks/months in order to avoid being identified by seers hindsight-walking to their homes, committed the crime, and then made a hasty getaway out of the country, where the seers can't follow them to their current location. Sometime later, they can come back home.
There is another possibility when dealing with not-so-long-ago hindsight (a day, for example): poison. If the criminal has access to slow-acting poison, they can use it without fear of the seers, since the seers won't be able to see who poisoned the victim.
Few Seers / Average can look > 1 day, week, month into the past
In this case, the seers will be stretched thin and won't be able to investigate every crime. They will probably be put in a taskforce of sorts, focusing on high profile or otherwise important crimes. Therefore, lower level crime will still exist for the most part, while high profile crimes will probably be very few and far between, or have to be aided with magic to shield the perpetrators from hindsight.
The exceptions are mostly the same as in the previous section. Indeed, in this case, poison becomes especially handy: you can use a relatively short-acting poison so long as its symptoms can be confused with accidental or natural deaths (causes a heart attack, for instance). With few hindsight seers, the police will have a good chance of simply assuming it was a natural/accidental death and move on. Meanwhile, if there were many seers, the police might have seers do a cursory look into the victim's past just to check for such foul-play.
Many Seers / Average can look < 1 hour into the past
There probably won't be much petty crime, especially in areas near police stations. However, high profile crime probably won't be much affected, since these tend to be at least a bit thought through. If all you need to do is get an hour's head start on the police, anyone with even a modicum of discipline can probably do it. Kidnappings will probably not be affected either, since you probably can't follow the victim's footsteps in time.
Few Seers / Average can look < 1 hour into the past
In this case, the seers probably won't have much of an impact. They won't be able to stop serious crime and there aren't enough of them to make a dent on petty crime either.