There are a large list of places, but I'll do my best to summarize my findings after having played this game for about a month. All of the pictures that follow should be considered spoilers.
- Right in the beginning of Foyer, turn around and run into the wall. This secret is here 100% of the time. Notice where my camera is:
- Perks can help you get to some secrets: ,
- The finish room for Sanctum (I believe) has a bunch of arrows going up. This is a cue that you should jump up. I believe it takes nearly 10 jumps at the standard jump height to get that secret, but there is one there. There is also a secret in the finish room for Foundry:
- The warehouse is dark, but there are some secrets to be found by jumping in the corners and off in the distance.
- Look around. Many secrets are found in very small nooks and crannies near the edges of the rooms, and you can often see a small entrance after close examination. For example, to the right of my cursor is two secrets. One you can walk into, and one you have to jump to:
- Don't feel stupid trying to run into walls. If you see a path that looks like it goes into a wall (Gearworks has a lot of rooms that have this feel), run into them. You never know; you might go through them.
- Turn around once in a while. You can miss a lot of secrets by not looking behind you:
- Look up. There are so many secrets that are up. The Bluegrass perk helps you with this, since you start with 3 extra jumps. Additionally, The Motivator and the Pocket Thruster are the best items to help you search up. , ,
- Look under platforms and walkways. Sometimes if you are looking at a platform/walkway head-on you can't see these secrets, but they are often hidden right underneath other platforms/walkways.
As for your other questions..
Visual cues: look for holes in the wall, or paths that go straight into a wall. Also, platforms that you can't reach are often secrets. Most of the time, secrets are just out of reach or are hidden from plain view.
Repetition: secrets are not always repeated throughout plays, but this is because the rooms vary even across plays. You might recognize several parts of a room being the same from play to play, but the overall room will change. Oftentimes these parts do contain the same secrets from play to play, but not always.