Come to think of it, I once had a tipsy old man sitting next to me on the train ask me to look at his haiku.

Literal

Come-to-think-of-it, train [possessive-の] inside [at-で] next-to [at-に] sat tipsy old-man [by-に], own haiku [object-を] look-at want [quotative-と] was-told thing [subject-が] exists.

A charming anecdote built on ~たことがある (have experienced). The relative clause 隣に座ったほろ酔いのおっさん packs a vivid scene before the noun. ~に...と言われた is the passive of indirect speech: 'I was told by X that...' ほろ酔い (pleasantly tipsy) and おっさん (middle-aged guy, casual) add color. そういえば (come to think of it) launches the memory.