Can we account for every year by constructing a time line from primary evidence or is possible that early record-keepers or historians made errors and at some point a year or more has been added or omitted?
For example, we know that 100 years have passed since 1919 because there are verifiable records that each intervening year occurred. But are we certain that 1000 years have passed since 1019 and 2000 since 19CE? (Note this isn't a question about determining the birth date of Jesus, but whether exactly 2019 years have passed since whatever year was chosen as 1CE).
Yes. There are records from multiple places that can corroborate the current dating system including records from Rome, Byzantium, the Islamic Caliphates, and China to name some of the major ones. These documents comprise of mostly administrative records that allow historians to piece together timelines of important events down to months, weeks, and days. The tricky part is converting other dating systems into the present one we use, but specialists have already done that legwork.
Does it really matter? Not necessarily. Our concept of time is relative to other points in time we think are important and/or useful. There is no Universal clock somewhere that has the correct time of humanity. If, on the other hand, you are asking if somehow humanity has simply forgotten the past of one or two years, the answer is no. The world would had to literally shut down for there to be such a huge gap in the historical record. Multiple societies have overlapped over the last few thousand years that give historians a good sense of time. Even though the records are sparse by comparison to today, there is still more than enough to prove what you are asking.
Hi, you may be interested in some earlier answers
Not discouraging further answers, but this one from u/sunagainstgold may be of interest to you: