Many years ago I received a conviction for possession of a shotgun without a certificate.
You may think that rules me out entirely.
What happened was that I already owned it, and a certificate, which expired without my noticing. After about a month, I realised, and took the shotgun to my local police station while I applied to have the certificate renewed.
No problem with either - but they took me to court, I paid a fine of £30 (no more than a slap on the wrist) and we all carried on as normal.
That was slightly more than a caution - but only slightly more. Hasn't ruled me out of a flying career.
No problem.