Nonconstancy of error variance If the residuals show that the non constancy of the error variance is clearly present, does it mean that your regression results are completely invalid?
 A: It depends on which results and what you mean by valid/invalid.
The coefficients are still a measure of a line going through the center of the data, so the line itself is still meaningful.
The relationship between the mean square error and the variance of the residuals becomes more complicated since there is not a single value that is the variance.  But if you can model the variance then you can get a meaningful relationship using weighted regression.
Standard prediction intervals (based on ordinary least squares, not weighted least squares) will be too narrow in some areas and too wide in other areas, so would probably not be considered valid.
Tests and confidence intervals based on the standard assumptions are not going to be exact any more so p-values and confidence intervals will be approximate, whether that approximation is close enough to consider them valid, or potentially bad enough to consider them invalid will depend on the amount the variance varies and your personal preferences.  Proper use of weighted least squares (or other methodologies) will help here as well.
A: You should not make any inference when the variance of your residuals are not constant. See for example page 243 of Practical data analysis. This is mainly because the estimated standard errors of your coefficients are not reliable. And that makes your $t$-test (or $F$-ratio) invalid.
