I have had a few issues with MTI, and I made some Github issues about them:
#503,
#560. It also does not play nicely with abstract models, or model mixins. I have found that the easiest way of mixing in extra functionality to your Page models is to make an abstract Model (not Page), and mix that in with a Page, otherwise you get strange clashes with MTI fields. Performance is another issue, and iterating over a Page queryset calling Page.specific on each one will use a huge number of database queries.
PageQuerySet.specific (coming in 1.1) can help here, significantly reducing the number of database queries required, but traversing ForeignKeys to a Page will still need an unavoidable Page.specific call.
Wagtail does integrate with caching layers such as Varnish or Squid quite nicely from what I have heard, so if performance of plain Wagtail does become an issue, caching could save the day.