Greetings all. Visit the following site to resolve any timing related issues with the game (among other things.)
I'm not sure if GOG or Activision collaborated with the makers of these patches for this particular version, so I felt I needed to impart this information so everyone can get the best possible experience from this game.
http://www.sierrahelp.com/Games/GabrielKnight/GK1Help.html
Happy playing. It's without doubt one of, if not the, finest adventure series of them all. I repurchased it on GOG to support the cause.
Keep an eye out for Jane Jensen's brand new adventure series, Gray Matter, being released soon.

Any fellow GOGers commenting on whether or not we need those patches?..

In this forum I see a question relating to the section where Gabriel needs to scurry past Frick, the desk Sergeant, while he's distracted, to get into Mosely's office. A timing-related issue on fast computers.
Since this player is having problems here, it is evident that the NRS patches aren't implemented in the GOG version. And since GOG is clearly running the game through DOSbox, using this on its own won't solve the problem.
But, as I've mentioned, there are other tweaks on that site that I highly recommended.

Well, I don't know if the timing problems are still present at the GOG version; all I can say is that they DO were on my old DOS version, but, since you can set the game speed whenever you want at the settings screen, it's just as easy as to go to that screen, slow the game, do the task wich needs precise timing, and, once it is done, tune up the game speed again.