Having lived in Taiwan for a few years after being in the mainland, I might chime in here.
In my personal experience, the only times you won't be understood in Taiwan using mainland vocabulary is with food items like vegetables (e.g. 馬鈴薯 instead of 土豆). Otherwise, people will understand you, and even if you use somewhat different vocab or pronunciation, you'll slowly pick up and adopt the words and pronunciation they use. They might also point out directly some of the more glaring differences, like 垃圾 la ji instead of le se. There really aren't so many differences though, and there are lists online that you can look at too.
As far as dictionaries go, the English–Chinese dictionaries in Pleco aren't good about providing regional usage information in general, not just for Taiwan/mainland, but some of the Chinese–English dictionaries do mention it. So if you find a word in an English–Chinese dictionary, you can tap on it and see if the Chinese–English dictionaries say anything more (e.g. CC and Key mention that 土豆 has a different meaning in Taiwan). If you can read Chinese already, Cross-Straights is helpful. If a word is only used in mainland or Taiwan, they start the entry with 陸詞 or 臺詞, and if pronunciation differs, they clarify with arrows (pointing right for Taiwan, left for mainland). It's always good to remember though that dictionaries never give you right answers, just things to try out. Trying out a word in conversation (or asking your tutor about it) and reading/listening to how others use it is when you find out if it's the right word or not.
If you take Chinese classes in Taiwan, something else to be aware of is that TW and Mainland traditional character sets are not completely the same, so make sure to choose a TW font for Pleco.