As my Year 11s will attest, the use of ‘however’ commonly introduces a contrast or opposing point. It can, of course, present a different take or slant on a previous argument. It doesn’t, however (!), suggest that the upcoming point has the same qualities or emphasis as the previous point(s).

An example.

http://www.thisishullandeastriding.co.uk/hotels-and-travel/travel-agents-and-services/humberside-airport-travel/business-10648962-detail/business.html

In this piece of marketing, the opening paragraph states:

Established in 2005, we have been catering for all of your travelling needs for over 7 years. However, we bring over 100 years of total travel industry experience to the table. (their emphasis.)

Surely the indication of 100 years of ‘total travel industry experience’ is a positive point? It indicates a level of nous and wisdom that comes with age and experience. However (!) are these not the same qualities indicated in the fact the shop has been open for 7 years? Here, the use of ‘however’ is used inappropriately: ‘moreover’ or ‘furthermore’ might have been better choices. Even better, though, would have either been no connective at all (seeing as they will act as two opening statements) or the use of consequence connective with some modality (therefore, we are able to…)  The last choice gives sorely missed context to the first sentence (particularly as they don’t mention their name!)

Beware two statements following each other when opening a paragraph – would one do?

I doubt, though, that this really matters to anyone more than English teachers with too much time on their hands.