Let's say you take a snapshot at location A - while your GPS is currently +/- 10 m off (but potentially 30-50m), and currently jittering at 1-2 mph.

Then walk to location B and take a new position - even now having the GPS jittering around at maybe 1-2 mph.

This jittering at 1-2 mph should give you an idea how your distance measurement will be affected, since that tells you that the GPS don't jump 50m off in 5 minutes but can glide around quite quickly.

So you can have 10-100m error already within 10-20 seconds.

A number of GPS tends to behave better after you have started to move, where they use Kalman filters etc to try to even out the jitter. But most GPS are very "noisy" when you are standing still.

Alternatively, you could have a couple of mm up to maybe 1m error even after months, if you had a differential GPS that could retrieve corrections computed from a static location not too far from where you are (since some of the GPS errors are very local - mainly the lens effects that makes the transmission from the satellites bend and take a longer route down to your receiver).

I'm not sure if it is applicable in your case, but potentially you could get better results with a GPS with support for inertial navigation. They are mostly intended for dead reckoning when you need to support tunnels or (city) canyons where the majority (or all) satellites are hidden for significant times. But maybe, just maybe, there are receivers that also uses the magnetic field, graviation and rotation to cancel out and average the random jittering. Inertial navigation would know when the satellite signals indicates the wrong travel direction or too high/low speed. An interesting thing - even a "standard" phone like Samsung Galaxy S II contains a huge set of sensors. It's just a question if someone have spent the time making full use of them (and how much they want for the application).

The initial issue here: What is your volume, and how much money?