Detecting the presence of measurement error When can I know that I'm in the presence of measurement errors? i.e., when can I know that I should use a measurement error model(error-in-variables model)?

Are there any statistical tests for checking that?
Suppose we observe only $\tilde{x}$ and $\tilde{y}$ which are the true values measured with error:
$$ \tilde{x} = x + u$$
$$ \tilde{y} = y + v.$$
We would like to estimate:
$$ y = \beta x + \epsilon$$ but all we can really estimate is
$$\tilde{y} = \hat{\beta} \tilde{x} + \zeta$$

However, if  y is measured without error ($\tilde{y}=y$) we can use reverse regression to bound the measurement error in regressions. The regression is:

$$ y = \hat{\beta} \tilde{x} + \epsilon$$

You also run the reverse regression
$$ \tilde{x} = \hat{\frac{1}{\beta}}y  + \hat{\frac{1}{\beta}}\epsilon+ u$$ 
Define the reverse regression beta as $\hat{\beta}_r = \frac{1}{\hat{\frac{1}{\beta}}}$. It turns out that the results from
the standard regression and from the reverse regression will bracket the true
coeffcient, i.e. $plim\  \hat{\beta} \leq \beta \leq plim\  \hat{\beta}_r$.

This interval is small when the variance of $u$ and $\epsilon$ are small. If one of the two are zero then one of the inequalities hold exactly. Unfortunately, in practice this interval may be large and therefore this approach not very helpful.