[bojan]

Yep, this is how the RA circle is designed at EQ6 (and EQ5 as well): slewing corrupts the RA setting/calibration, while tracking doesn't.
The only way to use it is never to slew with motors, but always to push to the desired coordinates manually. And just make sure the tracking is always ON.
Also be careful which scale you are using - one is for Northern, other one (with opposite markings) is for Southern hemisphere.

Or, after slewing with motors, you should always adjust the correct RA.

The problem is, RA setting circle on those mounts is essentially hour angle circle, but coupled to tracking motor to compensate for passing of time and to show RA - which doesn't change with time, but hour angle does. This is the reason why slewing should never be attempted if you want to keep the RA calibration.
To obtain the similar functionality some more advanced processor equipped electronics setting circles have, it would require very complicated mechanical solution (including differential gearbox) - far too much expensive to be practical.
Declination circle is free from issues above.