There are times to search for specific years and there are times when we should not. Many searches at Ancestry.com allow users to include more than just a specific year as a part of their search. Before you mindlessly enter some search terms and click “search” think about that year and that range you entered.
If you know (reasonably) that a relative immigrated to the United States in 1850, you may want to search for 1850 immigrations allowing for an error of plus or minus two or five years, depending upon how reliable you think the 1850 date of immigration is. It may be necessary to broaden the search even more.
If you are searching for someone in the 1860 census whom you think was born in 1840, you may want to search for them as being twenty years of age, plus or minus a few years, again depending upon how reliable you think the year of birth is. The older a person is, the more likely their age is to be incorrect.
Newspapers may be a little different. Some would run a “days beyond recall” column, where items from 20, 30, or even 50 years earlier were re-published in the newspaper. Consequently a death notice from 1890 may appear in a 1940 edition of the paper. Do not assume that a reference to your ancestor 40 years after his death cannot be his. It may be that the paper is rerunning part of an earlier notice. Death notices typically do not appear thirty years before a death, but they may occasionally appear thirty years after.
Think about the record you are searching. How accurate does that date need to be? And it is possible that the range of years you are searching for needs to be larger than you think?