The difference is a subtle one yet the two are rarely interchangeable.

最後 means plain "last", the very "end" of a thing.　
「君はボクの最後の恋人だ。」= You are my last lover.
「田中は最後のサムライだ。」= Tanaka is the last samurai.
「今日が君に会える最後の日だ。」= Today is the last day I'll ever see you.

最終 signifies the "last something within a time frame".
「最終列車は00：20に大阪を出る。」= The last train leaves Osaka at 00:20.
「今日が今回のハワイ旅行の最終日である。」= Today is the last day of my Hawaii trip.
「好きなドラマの最終回は明日です。」= Tomorrow is the last episode of my favorite drama.

You can directly attach a noun to 最終.

With 最後, only very limited nouns can be directly attached (in fact, all I can think of now is 通告. 最後通告 means "ultimatum"), and with other nouns, you need to insert の in between.

hey thanks that's really informative sashimister

So what about things like "in the last letter...", "in the last episode...". They are not really in a timeframe, but you are not really sure they are the very last ones (there might be more letters/episodes or there might not). Basically assuming more a meaning of "previous" then actually last as final.
お願いします.

To say "the last letter", we don't use 最後 or 最終 in the first place if the correspondence clearly will continue. We say it この前の手紙、前回の手紙.

But if you really mean the "final letter", then that is 最後の手紙.

Same thing with "the last episode". Unless it's the final episode of a season, we don't use 最後 or 最終. We say it 前回.　　If it's the final episode, then it's 最終回.　　How can you be not sure if it's the final episode at least of that season? Isn't that announced? Anyway, it doesn't matter if there is another season. The final of each season is called 最終回.　This is the same with the "last train" (最終列車) of the day. It may be the last for that day but trains will be runnng the next day, too.　

hey sry if this is off topic but is 前々回 ever used?

The dictionary thinks so: “前々回”の検索結果（1 件）：英辞郎 on the Web：スペースアルク