I am a US citizen and had few minor immigration problems one time when I tried to enter back in 2018 but they let me in after all. Last year in 2019 I tried to enter again and they let me in with no problems. Does my last successful entry wipe my slate clean? I will apply for a tier 4 and I am just very nervous regarding my entry back in 2018 when they almost considered me a frequent visitor
No clean slate. Sorry. There is a general guidance that for some visa types, certain transgressions older than ten years may be disregarded at the case worker's discretion. That doesn't seem to apply to your case, and you will have to give some extra explanations as to why the UK can trust that you won't violate the terms of the Tier 4 visa. The fact that you entered again, and presumably followed the rules, does bode well for you though. This not only gives you a positive mark on your recent immigration history, it means that whatever happened in 2018 wasn't so bad as to invoke a ban or leave any major flags on your record.