There are really no differences between the accuracy of online family trees and paper-based genealogies of the past. Ironically, experienced genealogists tend to discredit and avoid online family trees and embrace inherited paper genealogical records when it is obvious that genealogists who were working before computers and the internet, even professional genealogists, had far less access to genealogical records than anyone has today.
When I first began doing genealogical research almost 40 years ago, I completely relied on paper family group records from the Family History Library in Salt Lake City, Utah. As I reviewed the work that had been done previously, I almost immediately discovered that the existing submitted (user-created) paper records were riddled with errors. The records created by experienced and, you might say, professional or professional level genealogists were just as inaccurate and subject to unsupported conclusions as those submitted (and copied) by the obvious novices. Even with the limited resources I had at that time, I was able to begin doing research into historical records and started trying to correct the errors. Interestingly, I am still doing exactly the same thing today but with more records.
For the past two years or so, I have been able to work with a core representation of my family tree copied from the FamilySearch.org Family Tree into my own personal family tree on MyHeritage.com. Using the MyHeritage Consistency Checker, I have been able to more accurately judge the accuracy of the information entered into the Family Tree. I must conclude that the accuracy is rather dismal. This test tree on MyHeritage has only about 4,072 people. The MyHeritage Consistency Checker finds 1,226 inconsistencies including some of the standard: child older than parent and child born after a parent dies. To say the least, this is disconcerting.
Granted, the automated error finding programs are not perfect but they do give us an idea of the depth of the problems that are endemic in all family trees. Could I create a completely error-free family tree? The answer depends on the number of individuals in my family tree, the time spent in doing research, the focus of the individuals selected, and the availability of historical, genealogically significant records. For example, if I were to confine my research to my direct line surname family, the Tanners, I could be almost certain that information I have already accumulated is almost completely accurate. But, if I add collateral lines and descendants, I will quickly get to the point in time when the number of people involved and the possible lack of records will begin to diminish my accuracy.
To maintain that your family tree is completely accurate, you would have to assume that all of the underlying source records were also completely accurate. Even if you are an extremely meticulous researcher, you ultimately must rely on the accuracy of your records.
Does DNA testing improve the accuracy of a family tree? Yes and no. If a home DNA test is done correctly and not contaminated then the resultant test will be accurate. Is a home DNA test as accurate as one done for a court case, i.e. a criminal prosecution? Not at all. The main difference is the custody chain. All physical evidence in a criminal trial in the United States is subject to testimony about the chain of custody. The attorney presenting the evidence has to be able to show every person or entity that had possession and control of the physical evidence since it was obtained. That "chain of custody" cannot possibly be shown to occur in almost all home administered DNA tests because the test results are mailed in to the testing facility and upon arrival, the person opening the test is not disclosed. However, for genealogy purposes, the accuracy of the test is adequate if supported by careful fully documented research.
It is often assumed that genealogical information obtained directly from an informant about people known to the informant is reliable. Bible records are one common example of this type of record. However, we can always speculate about the true father of a child or the accuracy of the dates recorded. People not only make mistakes but they also intentionally falsify records.
If we automatically discount online family trees any time they disagree with our own records, we may ultimately be assuming infallibility. Since being infallible is highly unlikely, we must always accept corrections to our data with equanimity. With careful research using all the available tools and aids such as DNA testing, we should be able to have a reasonably accurate family tree but that does not give us a license to dismiss all other online family trees as inaccurate despite their failure to have sources and jump through all the hoops we think are required for accurate historical research.