Is it acceptable to show summarised or cite movie reviews and ratings
from other websites?
Legally, it depends. In most countries, it is ok to quote/summarize when naming the source. Especially if you provide a link, it is unlikely that anyone would have a problem with that.
What SEO issues might I encounter?
Short-term, you might lack unique content. Especially in the beginning, I would make sure not to cite/quote too much but rather to paraphrase. While this would not create unique information, at least every paragraph would be technically unique content.
The main long-term issue you may face is that Google sees you as a site that just sends traffic to other destinations. In the past, Google has often tried to cut out such middlemen and send traffic directly to the destinations.
What you can do is try to be an aggregator that provides actual value. For example, by summarizing the reviews from multiple sources, including less common sources. If you only summarize the reviews from IMDB and RottenTomates, there is very little value for readers. But if you include genre-specific review sites or unstructured reviews written by journalists on news sites, you could create something that provides actual value.
on one page of my blog.
If you look at successful aggregators that summarize content from other websites, you will see that about 0% of the successful ones are blogs. A blog is most likely not the content format someone is looking for to get an overview of movie reviews. You can, of course, start with a blog and earn some rankings. But you are unlikely to become the number one movie review aggregator.