I am not aware of a way to calibrate the altimeter. It is also not clear to me how it gets the initial value that it displays (I assume GPS), but generally (and this has only been 2 weeks) it has been fairly accurate. But I can't tell if "looking" at elevation, by having a complication for elevation, impacts how regularly the watch is tracking elevation; or how much it depends on the iphone (and whether the phone has an always on altimeter/barometer as well).
You can calibrate the altimeter using altimeter+, but that does not change the value or reading of the built in altimeter, so changing the elevation in A+ does not change the value in the default complication. Altimeter+ supports Aster, and so I think that is built in to both the phone and the watch, but I am not sure about that either. But Aster is supposed to generally be more accurate vertically than GPS.
Before I got the S6, I used the app Up High for an altimeter on my S3. It was faster and easier than Altimeter+. I always thought Up High showed the continuously changing system value for elevation and barometric pressure, since that is all it does and the numbers bounce around up and down by a few feet continuously. But the values in Up High on the S6 do not match the value in the complication, so somewhere in the watch there are calculations that result in different elevation values between the complication, altimeter+ and up high.
Even without calibration, the feature seems pretty useful and pretty accurate. But I think we all need more testing and experience, particularly with folks driving to a trailhead that involves a significant change in elevation, and how accurately the watch accounts for that change (without a phone around) and then how it adjusts for that initial error in starting elevation in terms of how it calculates net gain. I have only done this once (and it was accurate in starting position).