You can't get to the end of the game without using a couple of forgotten moments, so you'll need to pick some up. This can slow a run down because you have to get them to actually show up before you can pick them up. To complete the game, you need to use ~67 in-game minutes, meaning you must use at least 2 forgotten moments, assuming you make no other mistakes like entering the wrong room.

The solution is to pick them up during 'interactive cutscenes', cutscenes where stuff is happening but you can still click around with the mouse.

The first easy one is in the greenhouse, directly after clicking the tomato with the slingshot, get the moment behind Skeeto's wings before the tomato hits the ground, you can't interact with anything while this cutscene happens aside from the forgotten moment, so it's worth getting it.

The second one is in the clock tower, after putting the lever in and picking up the battery, try and get the forgotten moment at the top left of the middle pillar of the staircase. You only have a short period of time to get this one, and in most of my runs I can't get it to show up in time before I have to leave.

The third one is gotten while talking to the mouse who's missing his dentures, you can easily pick up a forgotten moment behind Skeeto as this scene gives you plenty of time. This scene is also a good time to use all of the forgotten moments that you've collected thus far.

The last one I usually get is while Skipper is collecting the needle out of the drawer in the bedroom, the forgotten moment is right behind his head while he's at the drawer and you can pick it up and use it before he gets back to position.

You can usually memorize the exact point of the screen that you need to hover over to get the moment to show up, wiggling your mouse a lot can risk it not showing up at all if you go too fast, so it's better to try and get the location exact in your head so that you can get the moment immediately.