My biggest problem with the current software is the bad usability on mobile devices, particularly on smaller smartphones (on tablets/phablets, its "almost" usable but not very comfortably). I run a website myself and the percentage of traffic from mobile devices/small screens has increased to over 60% in the last years. This means that Bitcointalk is probably getting only half, or even less, of the public/traffic it could have.
A design refresh would also be for sure attracting new, potentially younger public, as would new functions like a better watchlist, where you could get delivered the complete posts instead of only the titles of threads who have been updated, so it's closer to Twitter's "following" model.
SEO is also an issue, like DdmrDdmr stated in one of the first posts; I was shocked that particularly in Spanish the visibility of the forum is so low.
What I'm not 100% sure is if I would like to have features like a "like button" system, like it was introduced in the German Coinforum. I was generally supporting these kinds of features, but a
thread by a prominent German forum user made me think about it - it could lead even more to a "popularity-seeking" discussion style marginalizing "unpopular" opinions, like we know it from other social media. On the other hand I can imagine that people familiar with social networks would miss such a feature (and no, merit isn't the same thing). Maybe one could introduce it but make it possible to disable it?
What should however be preserved is the BBCode system (there was a discussion about that some months ago). It can be complemented with Markdown but replacing it completely would make tons of old content inaccessible.
Overall I have voted for "yes", although I'm in favour of a "careful" transition, to not obstruct post habits that have been evolved, mainly related to BBcode formatting.