[I've been asked by the moderator to place my answer in the text box; I assume this is what is meant.]
I would use "of" in both cases. As a native speaker, in this context approval "for" is wrong.
Another possibility, if you want to use "telegramstijl" would be:
Proposed corrections and consequences: approved.

Off the top of my head (so to speak), I 'm tempted to say I would always use "approval of" although I can imagine there might be certain situations in which "for" could be used. For instance, "He sought approval for his plan." To my way of thinking, I would still use "of" in this context, although "for" would not sound wrong. If I think of situations in which "approval for" would be the correct or better choice, I'll let you know. Could also be a US/UK issue, but I'm unaware of that.

If you want to be kind to the translator and retain as much of the translation as possible, I think you could use both, since this concerns the *act* of approving -- in this case by by providing a signature. I would then use 'approval for' in both cases. As far as can see, there would be no need to discriminate between the two cases. Actually, though, I think the translations should have read:

For approval of proposed corrections and consequences: [signature]
For approval of the discrepancy report as drawn up: [signature]

In that, you would obviously have to use 'of' as well as 'for'. How's that for a neat 'political' solution? ;-)

The BBI Combinatory Dictionary of English [Benson et al, John Benjamins Publishing Company]:

approval (noun):
1. to give one's approval *for*
2. to nod; voice one's approval
3. to meet with, win approval
4. one's complete, unqualified; qualified; tacit approval
5. final; public approval
6. approval + infintive (we received their approval to continue the research
7. on approval (we bought it on approval)
8. (miscellaneous) to receive somebody's stamp *of* approval.

approve (verb):
1. approve *of* wholeheartedly
2. (D; intransitive) to approve *of* (we approved *of* his decision) [JdH: the abbreviation refers to a specific verb pattern]

Hope this helps!


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Note added at 6 hrs (2009-03-01 21:12:15 GMT)
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@Els: Zoals vaak is context belangrijk. Maar 'approval for' is zeker niet fout, en naar mijn mening in jouw voorbeeld zelfs te verkiezen. 'Approval for' levert overigens wel minder googles (14.400.00) dan 'approval of' (47.800.000). Daar moet je ook weer niet te veel waarde aan hechten, want de context bepaalt m.i. welke vorm je wanneer gebruikt. Overigens, die BBI is een standaardwerk op dit gebied, en JBPC is zeker niet de eerste-de-beste op het vakgebied van de linguistiek. Cheers!