The common bad boy of fermentation byproducts is diacetyl, commonly described as a butter/butterscotch flavor/aroma. This is yeast strain dependent (some English strains are notorious offenders), and also reliant on the temperature during the initial growth phase of the yeast (why many advocate pitching cooler, then letting your temp gradually rise). Chris White advocates a two day rest on p. 113 of Yeast: The Practical Guide to Beer Fermentation.
Other flavors such as acetaldehyde (green apple) should be completely consumed by the end of fermentation (it is one of the precursors of ethanol production: glucose --> pyruvate --> acetaldehyde --> ethanol), so, assuming complete fermentation, shouldn't be there in the first place. It can also come from oxidation of the pre-existing ethanol back to acetaldehyde, in which case you've probably got bigger issues on your hands from the oxidation. Quick searching doesn't reveal a specific timeline for acetaldehyde metabolism, but considering fermentation happens within a week or so, I can't imagine needing an additional week(s) (as advocated here in argument of cleaning up flavors) to clean up what should be an already minimal amount of chemical.
Just my thoughts. As always, if you're happy (and that includes making the people whom you're serving happy) with the beer you brew, that's the only thing that matters. Let your palate decide for you.