Testing for heteroskedasticity in panel data vs time series?
You can regress residual squares (from RE or FE depending on your estimation) on $X_{it} \hat\beta$ and its square using the clustered standard errors (the vce(cl id) option), and read the F statistic and the associated p value. This is basically the same as Het test for cross sectional models (White's simplified test).

xtreg y x1 x2, re
predict uhat, ue
predict xb, xb
gen uhatsq = uhat^2
reg uhatsq c.xb##c.xb, vce(cl id)
testparm c.xb##c.xb


Another test is for groupwise heteroskedasticity proposed by Greene (2000). This test assumes that the variance of the error term is $\sigma_i^2$ (no heteroskedasticity over $t$) and then test whether $\sigma_i^2$ is the same for all $i$. You can do it using the xttest3 module. The xttest3 manual says: 


  In terms of small sample properties, simulations of the test statistic have shown that its power is very low in the context of fixed effects with "large N, small T" panels. In that circumstance, the test should be used with caution.