What is the counterpart to overheard, when I did not heard, but read something in passing? Overread is rather the opposite, namely
To read over, or peruse.
Possible alternatives I could think of are notice and found.
I would say "came across", as in:
I was reading the New York Times and came across an interesting piece on....
Probably to glimpse may fit:
v.intr. To look briefly; glance: glimpsed at the headlines.
Espy - to catch sight of.
You can use it in several contexts.
I accidently espied a weird word while looking for a word in the dictionary.
I espied a new fact while turning the pages of her notebook.