Both are correct; you would choose according to context.
The first suggests that the fall is the topic (i.e. you are explaining the circumstances of a fall, for example to a doctor) while the second suggests his play is the topic (you are describing his play in the field, and mention the fall as the next event in a sequence.)
The ambiguity of the sentence structure arises because "when" has slightly different meanings in the two contexts. In the first sentence, you use "when" to introduce the answer to a potential question:
When did he fall down?
He fell down when he was playing in the field.
In the second sentence, the word "when" is actually used in place of the now-uncommon "whereupon," meaning "at which time":
He was playing in the field, whereupon he fell down.
In speech however, the second sentence could convey the same meaning as the first, provided emphasis is place on the first clause, especially the gerund and noun playing and field. In this case the sentence-reversal is used to emphasise the circumstance of the fall by bringing it to the beginning of the sentence.
I would imagine that whoever told you that (1) is not correct did so based on a prescriptive rule against double negatives. The advice is mirrored here on a list of common grammatical errors in English, and here in an English for Dummies book excerpt. The problem, however, is that it is kind of silly to take something that people say all the time and declare that it's ungrammatical. I don't know of anyone who would hear the sentence "I can't help but think that he's a criminal," and then wonder whether I think he's a criminal just because of the double negative between cannot and but.
As far as I know, (2) is correct, but nowadays it is not usually said or written, except when trying to achieve an overly formal or old-fashioned tone.
For (3), the sentence is correct and is largely interchangeable with (1). This page claims that (1) is primarily used to mean:
I am forced to the conclusion that S[, though I'd rather not believe it].
(or)
I am forced to the experience of S[, though I'd rather not have it].
(where S is some sentence, and the sense conveyed by the braces is optional), while (3) can either take that meaning, or:
I'm always thinking about [the fact that] S[, though I'd rather not do that].
I can see the point, but they both sound fine in either usage to me. Maybe that's just my experience.
One final remark is that all three of the constructions would have a certain formalism to them if spoken; I imagine it is much more common to use the contraction can't in place of cannot in that case.
Best Answer
In both cases, the word really implies the speaker thinks his audience may be labouring under a misapprehension (about the specific plan, or the fact of having any serious plan at all).
Note that both OP's examples are generally considered informal/non-standard. Thinking to do is far less common than the "standard" forms thinking of doing (or about doing).