Since all the learning programs like Pimsleur, Rosetta Stone, etc. teach Mainland Chinese with the accents and vocabulary that go with it, is it still a good idea to put all the effort into learning with them? I have Rosetta stone but kind of got discouraged after I kept finding out my vocabulary and pronunciation were inappropriate here. Should I go back to it?
You’re asking me if Ro$etta $tone is a good idea for learning Chinese? For my money, it’s not good no matter what accent you want. But my views are fairly well known on the subject. 
The main thing with acquiring Chinese is not the specific accent you pick up; it’s knowing the principal structures and highest frequency vocabulary of the language dead-cold. If you really, really, REALLY know those things (I mean deep in your subconscious knowing, not “I can figure them out pretty quickly” knowing), you will have enough extra brain resources to deal with accents fairly easily. The main barrier to listening comprehension in Chinese is not accents but too-superficial knowledge of the words and structures (aka, the language was learned, not acquired).
As for your own speaking, my own tired dissertation and MA theses showed that in Taiwan, a foreigner who is identified as a foreigner will be rated more highly on some psychological measures if he uses a “Mainland” accent. People may comment on it, but they usually won’t take it badly. Having a strong Taiwanese accent will probably suggest that you have spent a long time in Taiwan and/or have a strong Taiwan orientation, and will gain you some points in those regards. But all in all, IMO it isn’t important enough to worry about much, unless you will be spending a long time in Taiwan and get tired of the comments, or you want to hang around with some really grassroots extremist nativists.
I am definitely in a position to comment on this one.
(note: in all of this I have been working full time, study part time on average maybe 10-12 hours a week)
I started using Rosetta Stone about 1.5 years ago for my chinese. I used it for roughly a year, fairly consistently. I did all of disc 1, about 2/3 of disc 2, and the first half of disc 3.
I also used flash cards (Anki, then Pleco), my wife/friends helped me on pronounciation and to answer questions.
I built up a ‘solid’ basic understanding of the language with almost no conversational skills.
Last month I started taking private lessons and have had 9 (I think?) 1 hr 40 minute sessions. My conversational skills have skyrocketed, and if it’s simple topics then I fool people into thinking my chinese is good and they will typically respond at native speed, which backfires on me very quickly and I have to say my chinese is horrible can you speak slowly and use simple words 
Anyways, I am quite happy with my progress. The only thing I would do differently is start private lessons about 3 months earlier than I did. Rosetta is great for pronounciation and basic structures. The only downside is that you have to relearn some words, but it’s not all that horrible.
My recommendation: Rosetta Stone Disc 1, maybe the first half of disc 2, then go to lessons because after that it’s lost it’s value.
One more thing: DO NOT USE PIMSLEUR, it is a heavy mainland accent and words. You’ll be talking like a pirate. Rosetta tends to be pretty neutral. I have zero issues with people understanding me. I can either say it or I can’t, if I get a ‘huh’ it’s rarely because I messed up the pronunciation.
You seriously don’t need to worry about that!
The concept is literally like American English v.s. British English.
As long as people can understand you…language is a tool for communication!
I think the best is to learn the language til a certain extent where you feel like you know it well enough,
then you can try to get into learning the Taiwanese accent and vocabularies, as you’ll less likely to get confused,
and you’ll know different words for the same thing, great!
I’m Taiwanese, and my English was taught by an American teacher.
Then I came to England to study at 15, I didn’t have problems whatsoever communicating with people.
English people did occasionally comment on my ‘American accent and American spelling’ but they understood me perfectly and that was the most important thing.
I’ve gradually adapted to English accent and spelling over the years, now my American teacher tells me that he finds it funny and freaky that I sound like English!
If you live in Taiwan, the accent and the use of words would be influenced in some ways anyway.
So don’t get too worried about learning Mainland Chinese instead of Taiwanese Chinese,
and as stated above pronunciations in Rosetta Stone are pretty neutral,
I’ve found it a good source for learning languages as I use it for Spanish and French.
So, no worries, keep up the good work!! 