I am from mainland China,and I knew some taiwanese when I was in vietnam.I can tell you what I know. I think most taiwanese's mandarin is very easy to understand,but some people far from policy centre maybe have their own diarects.
some taiwan mandarin tones are little different from mainland mandarin.I had taught mandarin of taiwan version before.some pronounciations rules differently. and also some words,for instance,台湾普通话的版本里写着“课业”,可我觉得大陆不怎么用这个词,大陆常常用“功课”,但你不难理解它的意思。
I think I can expain it partly:
60years ago,because of the war,many mainland people come to taiwan ,they took the standard mandarin education to taiwanese.
in the long closed time,mainland and taiwan can't contect with each other ,with political and scientifical and cultural and geographical changing,they developed different useing words .especially some new facts and things.if you want to know what they are,you can try to find it from some taiwanese website(such as,台湾与大陆的用词对比),because I saw that list from a taiwanese friend before.或者,台湾与大陆表达习惯的不同,or you can search some books.Chinese have many many words,and almost every chinese character has its meaning.so it is very easy to understand what taiwanese are talking about.
supplyment,some taiwanese can speak taiwan tongue,some can not.so some of them would talk in that tongue,it is as same as some province people speak their tongues ,and I cant understand even a word.because they use them thousands years ago,so some of them are quite different.