There is no such thing as Taiwanese Mandarin. The Mandarin they speak in Taiwan is the same one spoken in mainland China (aka Standard Chinese). Perhaps you mean the Taiwanese Hokkien dialect, which is also one of the dialects spoken in Taiwan? They're both extremely different from each other.
As far as I understand it - the Mandarin spoken in Taiwan is the Southern accent/dialect.
Shenme is sometimes said "senme".
My teacher looked down on my southern accent (since i learned it from watching shows out of taiwan) and tried to teach me Beijing dialect - his native dialect - which is also looked upon as most proper and prestigious.
Bejing dialect has weird R insertions (google the term). So "zai na li" becomes more like "zai nar?" and "sh" sound is a bit sharper. Oh and "kuai diar" for "kuai dian". Things like that.
I should add - Hokkien dialect is strange sounding. I can't understand it, but understand Mandarin just fine.
I guess your question may have been answered in the previous comments.
To start off, like Sakura have said there is NO such thing as Taiwanese Mandarin. The Chinese language has many dialects. The two main ones would be Mandarin Chinese and Cantonese. Cantonese is generally spoken in Hong Kong. Now in Taiwan they speak Mandarin Chinese. Taiwanese is a dialect that is also spoken in Taiwan. There are tons of other dialects in China. It depends the region and city you live in.