I find that I miss a lot of power-up spawns on blind turns where I am not fast enough to react to jump and get them. I realize their spawns are random, but are they completely random? Should I look for them every 100 m, every 250 m, or triggered my score levels or something else?
By how I've played, you usually get one during 500-650m and the second one is at 1000-1200m. Even further, you get into a mine, soon after you get out, there will soon be another power up. This is about how far I have gotten.I hope to get even further to find more power ups to improve this answer even farther.
Power-ups appear fairly consistently - once you've gone 600 meters (without any frequency upgrades) without a powerup, one should appear. Failing to collect the power-up doesn't seem to affect the distance that the next one appears.
Power-ups can't appear above rope slides or during mine cart sections, but the distance traveled on those counts towards distance without a power-up and if you've reached the required distance in one of those areas the power-up should appear at the exit.
Gems and treasures always replace a power-up.
When using boost as your active power and power-up frequency are both fully leveled by coins: I find the best strategy is to only manually activate boost within a short window after the power-up spawn. Otherwise, you are likely to be boosting at the next power-up, making it extremely hard to collect.