Acknowledging funding originally intended for another purpose I am paid as a postdoc from two different grants that have been awarded to work on specific subjects. While these subjects are my main workload (both in terms of time spent and results achieved), I also work on the side on other (unrelated) problems.

When I publish these side studies, should I acknowledge my funding sources, given that that money was not awarded for the purpose of conducting that particular research? I have no problem acknowledging them, but I'm worried that by doing so I might give the impression that I'm using the money for what it was not intended.
This depends very strongly on your position and the nature of the grants.  The main deciding factors are:


Is your time clearly accounted to particular grants?  Postdocs are sometimes asked to fill out time-sheets that bill specific hours of work to specific grants, and sometimes simply "supported" by their grants.  If your hours are being specifically billed, then you must acknowledge funding on any publication that has had work billed to it (whether you should have done that is a different question).
How specific is the funding vehicle's mission and expectations?  For example, in the US, most NSF funding vehicles just want to see strong publications in an area plausibly related to the subject of the grant.  A DARPA contract, however, might be much more tightly focused and it could draw ire from the program manager if you appear to have been "wasting their money" on projects unrelated to the contract "mission."


The second point is very subjective and often depends strongly on not just the agency but the particular program manager and contract.  The PI of the grants should know the situation here, and be able to advise you on the preferred course of action.