Is measurement error in self-reported health a problem in this scenario...? I am running regressions to estimate the impact of health conditions on life satisfaction.

I have read a paper that showed that there is likely to be measurement error in the self-reported health variables in that those who do not work are more likely to report health problems to justify not working.

My question is, is this a problem for my estimates? I include various dummy controls to capture employment status so do I simply control for this potentially problematic bias due to measurement error?

Or, is the bias still there in which case I guess it would be a downward bias? Does my use of panel data and fixed effects make any difference?
Check the correlation between health status variables and employment status. Start with simple pairwise correlations and then perform auxiliary regressions where you regress a health indicator on the employment status variables.  

If there is visible explanatory power in employment status for health indicators, you may want to treat health indicators as endogenous variables and employment status as instruments. Depending on the number of variables, this may be the Two-stage Least Squares estimator.