Speaking from my personal experience with learning Latin, I found it to be useful in providing more in-depth knowledge on the construction of sentences, primarily the SVO sentence structure. English isn't my first language and I first learnt it formally when I was six or something like that. I absorbed English after being dumped in England at that age and didn't really know anything about grammar or anything like that; I knew how to make myself understood and that was all that mattered. Learning Latin actually provided me with this missing knowledge, as well as a load of other stuff.
Also, learning Latin does actually, subconsciously, made me able to sift through a large amount of unfamiliar words and efficiently identifying what is important and what is a 'filler'. In terms of vocabulary, problem solving and the like, I wouldn't say it increased my abilities in it; I'm still pretty crap in that regard regardless of whether I learnt Latin or not.
I loved learning Latin. It was a mix of learning the actual language and Classics. In one lesson, we would be busting whatever's left of my brain to translate tedious sentences. In another lesson, we would be watching 'Troy' and '300', more for fun than anything. That said, to denounce Mandarin as less of an importance to Latin is stupid from my perspective. Both have their own merits and pitfalls as a language.