We propose SUM-QE, a novel Quality Estimation model for summarization based on BERT. The model addresses linguistic quality aspects that are only indirectly captured by content-based approaches to summary evaluation, without involving comparison with human references. SUM-QE achieves very high correlations with human ratings, outperforming simpler models addressing these linguistic aspects. Predictions of the SUM-QE model can be used for system development, and to inform users of the quality of automatically produced summaries and other types of generated text.