Are there limits to how much data I can put in a dataset or scratch space?

The limits on dataset and scratch space (see note) files are documented as 

You can solve these problems with Domino Datasets:

1. There is no limit to the number of files that can be stored in a Domino Dataset.
2. There is no limit to the size of any individual file stored in a Domino Dataset.

ref: https://docs.dominodatalab.com/en/latest/reference/data/Datasets_best_practices.html#store-more-files-bigger-files-and-access-them-faster

Although not explicit, there is also not an overall size limit.  Datasets and scratch are a storage cost though, so best practice should be considered to keep these spaces as clean as possible and not indefinitely store data that is no longer needed.

Note: as of Domino v4.5 scratch space is deprecated as datasets have been redesigned to make them more intuitive and less complex to use.