I remember watching a show on the History Channel (when it was good) about snipers; and they had a segment about their training. IIRC they said the spotter is actually trained to look for the "ripple" to track the shooters shots and correct; as bullets don't always create a dust cloud or obvious impact. But, it's usually only observed under perfect conditions...clear, fairly calm, directly behind, etc.
However, I highly doubt that the shooter can see it since the recoil and any other movement probably keeps the human eye from being able to focus on it.

Here's a vid at full-speed where you can pick up on it; but it's still hard to see unless you really are paying attention:

First of all, I apologize if I come off sounding either insulting, or like a troll. However, this is just a bit too much.

First and foremost, every sniper is a spotter, and every spotter is trained to find and follow trace. Trace is what allows a sniper to fire and adjust. Snipers aren't supercomputers, nor are they Hollywood actors. Real snipers miss targets due to the vast array of variables that effect the shot, and thus a second shot is sometimes required. It falls on the spotter to find and follow the trace through his spotting scope so he can provide the sniper with an near instant mill correction, thus allowing the sniper to reengage within ~2 seconds. The conditions that allow observation of trace are irrelevant, what is relevant is all snipers know what trace is and know how to find and follow it.

I'm sure SWAT follows the same guidelines as FBI snipers. The FBI mandates that no shooter is to remain on-scope for a duration in excess of 30 minutes due to a degrade in reactions. When the shooter goes off-scope the SWS is passed to the spotter, and the sniper takes his place in spotting. Further, I've never heard of a sniper that was only trained to engage targets at 600 yards. The effective range for the .308 round is 800m, and military snipers are taught to to engage targets out to 1000m. The fact that most SWAT sniper engagements will take place inside of 100-200 yards is irrelevant. You're a sniper and as such must be capable of employing your weapon system to it's limits and beyond.

You claim to be a SWAT sniper, and I can't help but call you on that. You're either:
A. A SWAT like sniper from a 3rd world country that has little to no grasp of marksmanship.
B. A SWAT sniper that had seriously flawed training.
Or the more likely option: C. You're full of crap.

/rant mode off

Easy there killer, if your not law enforcement officer I'll forgive your lack of knowledge regarding LE precision shooting.

LE precision shooting is a whole different type of work then military sniping, which is commonly shown on TV. LE shootings normally occur well UNDER 100 yds. Most of the time it's under 50 yds. Most LE sniper/precision rifle schools usually only shoot out to 500 yds as very few facilities have the ranges to go out past 500-600 yds. The most recent school offered in my area only shot out to 200yds as that was the longest range available. Most of the time LE snipers operate without a spotter (sad but true), due to manpower and budgetary constraints. They also are on their rifle quiet a bit longer then 30 minutes (the first time I deployed with my rifle as a patrolman I was on my rifle for about 2.5 hrs before I was relieved). As far as being able to out shoot your weapon, again a myth. The majority of LE long riflemen are going to get probably a half day every month to practice shooting (while the assaulters do their own thing), and another half day during the scenario portion of your training day.

The reality of LE sniper work is you are there to gather intelligence 99.999%+ of the time. A good LE sniper school will stress this, and actually not spend that much time on shooting. There is very little need in the civilian context to be able to accurately engage a point target (1"-2") at more then 200 yds. The fact of the matter is that unless you're talking a hostage situation or a terrorist/WMD incident, there are few reasons to engage a suspect that's 100+ yards away from civilians and other officers. Shooting at 100-200yds with any high velocity center fire caliber (from say .223 on up) is mainly point and shoot unless you're talking extreme elevations, winds, or target movements. Like I posted earlier at 300+ yds is when you start to have TIME to observe trace. As Silverswift pointed out, at 100yds the flight time of the bullet make it almost impossible to observe trace at short ranges that LE traditionally shoots at. Also in LE you don't the option to adjust in your fire, you either make the shot or you don't. If you screw it up the first time, the opportunity is normally gone and the ability to correct your aim via observed fall of shot is not possible.

Personal experience time: I am not a LE sniper, I am however a patrol rifle certified officer, and I do shoot and train a lot on my own time. This includes High Power service rifle competitions (200-300-600 yds stages w/ iron sights), and various tactical shooting matches. I can guarantee you that the vast majority of LE snipers/precision rifleman/long distance interpersonal conflict resolution specialists, will normally deploy closer then I initially do on most calls. I've never been to a SWAT call where we opened up the inner perimeter, we always get closer once the big toys get there.

Longest distance I've ever setup my rifle: 79 yds (went back and measured it with a laser)
Bullet flight time: .0846 seconds (@ 2800 FPS)
Shortest distance I've ever setup my rifle: 15 yds (paced it off when we got done that night)
Bullet flight time: .0160 seconds

-Jenrick

I'm NOT a sniper, and unfortunately NOT an active shooter, but I am an enthusiast. Take whatever I say with that in mind. /disclaimer

I've read and and watched a lot of material on sniping, and most accounts of seeing the heated vapor trail from the round come not from the sniper, but from the spotter or instructors. (sometimes captured on camera too)

I'm under the impression that the vapor trail is more visible in hot and humid conditions, such as you would find in hotter months in the US Southeast. (Virginia, Georgia, probably Texas too) Can anybody confirm or deny that?

To quote myself: "You're not actually looking for the 1/2" bullet moving through the air, but the ripple of lower pressure behind it that affects the mirage. If you've got very high humidity you can get a vapor trail much like a super sonic aircraft (never seen a vapor trail personally, just pictures)."

So trace is not an actual vapor trail, rather a visible area of low pressure (much like a ducks wake in a pond). Trace technically always visible, however environmental conditions can mask it. A true vapor trail is when the low pressure causes condensation to form. As such just as you asked, the hotter and more humid it is the better the chances you'll see a true vapor trail.

-Jenrick