～する余地がある means "there is room for ～ing" and 精度を上げていく余地がある indeed means "there is room for improving accuracy". But the use of 余地がある is not very important to determine the correct answer here.
The critical difference between 3 and 4 is ～という and ～はずだ. Sentence-end ～という is used to repeat someone else's statement ("they say ...", "according to them, ..."), whereas ～はずだ is used to show the writer's own strong expectation ("I think they will ...", "they must ...").
Apparently, this article is written from the third person's standpoint, by someone who do not develop this system. Typically, this looks like a news article based on a press release from the manufacturer or an interview with the developer. In such a setting, in general, a writer (who is not necessarily an expert in this field) rarely gives his own technical opinion using はずだ in the middle of the article. Perhaps the writer even did not see the system before writing this.
Please re-read the question carefully, and see which fits the context better:
- 精度を上げていくはずだ ≒ "I, as an interviewer/writer, am sure that they will improve the accuracy (for some reason)" or "Everyone should naturally expect that they will improve the accuracy".
- 精度を上げていく余地があるという ≒ "According to the developers, there is still some room for improvement"
EDIT: To reach the correct answer, it is important to make a correct assumption regarding who wrote this article. There are a number of reasons to believe this was not officially written by someone on behalf of A社. In general, official announcements are far politer (です, ます, keigo) and use more formal wordings. For instance, compare this official announcement and this news article. They both convey the same information, but they look drastically different. Noticed that only the latter article uses という? Actually I'm pretty confident that this writing style is that of a typical technical news writer. Thus everything in the article is basically hearsay information based on another information source.
And most importantly, there is no way that one wants to use はず in an article like this, because はず expresses the speaker's subjective impression/understanding. If this were written by someone on behalf of A社 or in charge of the actual development of the system, concluding the announcement saying 精度を上げていくはずだ ("It appears that (or in our understanding) we will improve...") would sound totally irresponsible and funny. Instead, they should clearly state 精度を上げていく予定です, 精度の向上に努めます, etc. If this is written by someone not directly related to A社 (e.g., a writer of wired.com), suddenly saying something subjective like 精度を上げていくはずだ is out of the question, too.