Training Set: this data set is used to adjust the weights on the neural network.
Validation Set: this data set is used to minimize overfitting, and adjust the weights to retrain.
Testing Set: this data set is used only for testing the final solution in order to confirm the actual predictive power of the network
Test error is consistently higher than training error: if this is by a small margin, and both error curves are decreasing with epochs, it should be fine. However if your test set error is not decreasing, while your training error is decreasing alot, it means you are over fitting severely.
I dont think you have to be concerned about comparing Validation and Testing Errors. You should be comparing Training Error Vs Validation Error and Training Error Vs Testing Error.
Hope this helps!