On day 6, I'm trying to lure the fat cop out of the office so that I can get into Mosely's office. Unfortunately, the game speeds up as soon as he sets foot outside and he comes back in immediately.
I checked a walkthrough and apparently this is a known bug that happens on most modern computers? The walkthrough guy suggests downloading CPUKiller 2.0 off of www.download.com to slow down the computer's processing speed and, in turn, give the player enough time to go through Mosely's stuff.
Is this the only way to go or could the GOG folks find a way to make it work correctly by itself?

There is a different way to get past him. Just wait a couple of minutes after he returns inside and observe him.

Merci Syniurge, your solution was easy to execute and it got me unstuck! I even ended up beating the game yesterday!

GOG needs to be careful with its default DOSBox settings. They use "max" for cycles but Sierra games don't like this - it's much better to pick a fixed amount of cycles. It will avoid sound issues as well. If you set cycles to "10000" it should help as well.

Also, you can modify the CPU cycles ingame by pressing Ctrl+F11 to decrease, Ctrl+F12 to increase.
That's how I got past that particular scene :-D

max limit 20000
or so

Yeah, for the huge bulk of games on GOG that use DOSBox, 20000 cycles is enough. I used to set all the games I tested to "max" ("auto" caused some problems) but now I stick to each game getting its own amount of cycles.

help i cant seem to save the changes to the file

Copy the file to your desktop and make the changes - then move it back to the folder and overwrite.

My computer is apparently wildly over powered for this game. I had to both change the core to simple and limit the cycles to 20000. But after that it was perfect.

I did the same and yeah, no game-breakers after changing those settings. Some weird variations in Gabriel's walking speed in different places but nothing too annoying.
I think GOG should've at least set the core=simple value as default. Also I'm not sure if it's universal but the sounds improved a lot after setting the soundcard as "sb16" instead of "sb1", so that could've maybe been the default.

Thanks McDondo, this worked for me, and didn't involve messing with settings :P

Slowdown utilities should never be used with DOSBox, and are completely unnecessary. As mentioned, auto settings for core and cycles should never be used with Sierra games in DOSBox. Cycles are usually best set at around 10000. Even this is too fast for some Sierra games. There is also a fan made patch for speed issues with this game.

sweet, i just ran into this issue, I'll give these solutions a go when I get home today. Thanks everyone!