You could manually check all gradients e.g. via:
for name, param in model.named_parameters():
    print(name, param.grad.norm())

(or any other stats, if norm is not desired).
However, this approach would be quite limited and more sophisticated algorithms for model interpretability can be applied by e.g. Captum 109.
Also, you might want to plot the histograms of the gradients in TensorBoard or any other visualization tool, which should give you more insight into the model training.