You are right that LSTMs work very well for some problems, but some of the drawbacks are:

• LSTMs take longer to train
• LSTMs require more memory to train
• LSTMs are easy to overfit
• Dropout is much harder to implement in LSTMs
• LSTMs are sensitive to different random weight initializations

These are in comparison to a different model like 1D conv nets, for example.

The first three items are because LSTMs have more parameters.

You are right that LSTMs work very well for some problems, but some of the drawbacks are:

• LSTMs take longer to train
• LSTMs require more memory to train
• LSTMs are easy to overfit
• Dropout is much harder to implement in LSTMs
• LSTMs are sensitive to different random weight initializations

These are in comparison to a simpler model like a 1D conv net, for example.

The first three items are because LSTMs have more parameters.