I don't think there is a grammatical mistake.

If you don't like the way it sounds - and I agree that it doesn't sound particularly smooth - you could try "Forbidding children/young people/etc. to play in front ..."

Doesn't it also sound funny because of the other meaning of 'forbidding', or is that just me?

It's just you! *g* Seriously, you mean menacing or repellent, right? Wouldn't that be fobidding play rather than playing?

True, but as the sentence wasn't that good in the first place my immature mind immediately thought of

Forbidding playing is a good way to solve the problem. Nice playing is not.

Would that be just bad style, or is it simply wrong?

(This very much reminds of me of German signs saying things like 'Das Spielen der Kinder im Hof ist verboten'.)

Besides the solution in #1, other possibilities might be:
Forbidding play in front ...
To forbid playing in front ...
To forbid play in front ...

Or, you could turn the sentence around:
A good way to solve the problem is forbidding playing ...
... forbidding play ...
... to forbid playing ...
... to forbid play ...

When the sentence is turned around like the latter, what your critic or teacher may be critical of is:
1. lack of parallel construction
A good way to solve the problem is to forbid ...
A good way of solving the problem is forbidding ...
2. grammatical subject of the sentence ("way") is not the actor doing the solving or forbidding:
A good way for the parents to solve ... to forbid ...

@4: I can't say it's wrong, however I would not (and did not) initially recognize "forbidding" as an adjective in your first sentence. It was only when I read your second sentence that I realized where you were going. Does that answer your question?

Two -ings in succession is always bad style, and sometimes ungrammatical. Here it's just bad style. All you really need to do is to say: To forbid playing...

(Where gibson got her curious idea from, I really don't know.)

"Forbidding playing ... is a way to ..." actually sounds more natural to me than "To forbid playing ... is a way to ...". I'd use the infinitive in sentences such as "It would be stupid to forbid playing" or "To forbid playing would be stupid".

How about "Prohibiting games in front of ..."?

@SD3: It does, kind of, yes. Thanks.

@escoville: I come across 'forbidding landscapes' and the like much more often than people forbidding other people to do something, so my first association is usually the adjective. A simple question of what you're used to, I guess.