In my application, there was a clerical error that I managed to correct for in my printed application in relation to the question "Have you been refused a visa for any country, including the UK, in the last 10 years?". In particular, the online application was stated "NO" but I managed to correct it in the printed form to "YES" and I gave my attached reasoning as "Missing document" with pen. That said, apparently the online requires three more follow-up responses (country, visa type and date) which I did not managed to account for in the printed application form since they were not available to me on the paper when I was in the application center when you switched to Yes. Would this cause them significant difficulty (p.s. I only had one refusal in the past which was a Tier 4 UK visa).
It may cause some difficulty, how significant will be determined by the ECO who reviews your visa application. Applicants are expected to be truthful in answering relevant visa questions. Omitting an earlier, failed application, whether done mistakenly or deliberately, and whether corrected subsequently, may be cause for a refusal. More seriously, it could also affect future visa applications.
Depending on the outcome, as well as the reasons for any refusals, you may want to consult a UK solicitor which you can locate through the Law Society search tool or through the search option of the Immigration Law Practitioners' Association.