Kepler's conjecture concerning sphere packing is famous for having a proof, where referees got persuaded only after formal verification. Are there any other proofs originally claimed in full on paper, which went through similar process from doubt to acceptance, not necessarily through formal verification, possibly just through time?
On the other hand Mochizuki's proof of abc conjecture seems to come up as an example of a proof too frustrating to verify or completely refute. Are there any other ongoing examples where the work is too complex and with doubted results, but neither finally disproved or proved? I consider Mochizuki's work exemplary as compared to other false/too complex proofs, in that there is ongoing work and relatively recent seminars dedicated to understanding the techniques. Another example of this phenomena might be Classification of finite simple groups, many people still prefer proofs of theorems not assuming CFSG, because the full proof is too complex. I haven't encountered another theorem used widely with this attitude towards the result.