It doesn't really matter. All GMs are good at blitz but they're GMs lol. Anyway practice is really the best way. I used to be really slow but after a while I got used to moving faster. Tactical vision is a pretty big point too.
Is bad blitz play a problem?

Yeah, that's a good point. You can be thinking strategically but if you've overlooked a quick tactic it can screw your plans up very quickly. Maybe I need that tactics trainer thing.

Blitz is worthless. A player with a strong over the board rating and weak online blitz rating is significantly strong than a player with a high online blitz rating and low over the board rating. The reasons are plentiful:
1) Players with bad connections will lose games for no other reason than their connection.
2) Online blitz simply says you can move a mouse fast. If you spend 4:30 to get a 2-pawn up winning position, the opponent can easily time you out. In any real event, there's either a delay or increment involved, where the board dictates the result rather than the clock.
3) The ability to reason thru a position with serious thought shows a sign of better calculation and positional play than simply being able to see 2 or 3 move tactics in a few seconds. The blitz guru finds some cheap shot tactic, but has no clue what is going on long term.
And you ask about high level players that suck at blitz? I raise my hand! While my "blitz" rating over the board is 2069, it only existed since this year. Before that, all chess under 30 minutes was "Quick". Now Quick has a minimum of 10 minutes and blitz is lower than that. My Quick is only 1963, and has been as low as 1822. My Standard is 2124. Here on Chess.com, by Blitz is 1670, and about the same on ICC.
This should answer your question DrGero.
Look through some blitz tournaments with super-GMs. Even they miss tactical shots, especially during time scrambles.

Thanks for the comments. Glad to hear blitz isn't seen as that important.
Nothing is more frustrating for me than making blunders for no reason.

>> Is bad blitz play a problem? <<
Only if you have some blitzing title aspirations.
Joking aside, from personal experience (as a still very weak player) I would say that playing slow chess is definitely more helpful than blitzing in improving your game. You have to have quite a good vision and tactical understanding not to get slaughtered and overwhelmed in blitzing. So as a beginner do play slow games first, then start with shorter time controls.
Short games are definitely good once you have developed a little bit of playing experience and acquired some vision. Very good to play and train your opening repertoire, for example.

No one's game increases in strength when playing blitz vs. standard, so to that extent, no, it's not a problem. However, a strong blitz game is indicative of a strong standard game, because it shows how quickly and naturally you can make positional and tactical calculations. The better you are at that, the more time and brain power you can devote to the subtle nuances of a standard game, making it more likely that you will emerge victorious.
My blitz chess has always been terrible compared to my standard play from ever since I can remember playing. I seem to make blunders all the time when playing fast and I have a tendency to look too deeply into individual lines at the expense of considering all options.
So firstly, does it matter? (A philosophical question I know but let me know what you think)
Secondly, is there a way to overcome this problem I have?
And finally, do you know of any high level players who are great at normal chess but bad at blitz?