See this and this for example.

It seems that sometimes after writing an equation on a separate line with Latex like [dollar][dollar][equation][dollar][dollar], the next equation written inline like [dollar][equation][dollar] doesn't work.

From some experiments it seems like Codeforces internally changes single dollar signs to triple dollar signs if there is a match, and uses those to delimit Latex. I suspect the double dollar signs screw up the parser and after an inline equation, the single dollar signs won't get converted.