Sometimes, with a little bit of digging, the correct data can be located. I've had marginal success contacting municipal officials who had historical records available - some are willing to help and others won't respond at all.
Historical societies often have data available, too. A historical society in Outagamie County, Wisconsin, has the history of the county available online, and with some careful searching, I was able to find information about a bridge over the Shioc River that the local officials knew nothing about - except that it was there.
Google is your friend.
The National Bridge Inventory data is not always very accurate, but for many bridges it's the only convenient source available. Many times the year built is merely a guess. On the Browse by Year page ( http://bridgehunter.com/category/year/ ), notice that there's a jump in the number of bridges listed under 1900, 1915, 1935, and other years ending in 0 or 5. Most of these are probably guesses, and are probably wrong by several years or decades.
However, for years NOT ending in 0 or 5, the data is usually pretty good. There are a few oddball cases, though, where the year actually refers to when the bridge was relocated or reconstructed, not when it was originally built. I've also seen weird cases, especially in Arkansas, where the year refers to when the bridge was added to the state highway system, but it may have been built by the county much earlier.
For truss bridges, a very general rule of thumb is that pin-connected designs were built before 1920, while bridges with lots of ornamentation were probably built prior to 1900. But there's always exceptions.
Incorrect dates in the NBI are no real surprise. I have added bridges to the site where historical records conflict with NBI build dates, usually by a couple of years. The NBI lists another bridge I recently added with a build date of 1935, but the WPA plaque identifies the bridge with a 1941 build date. (I tend to believe the NBI in that case.)
Last week, I posted a bridge that was built in 1905 and there is a photograph of the bridge taken in 1908. NBI lists the build date as 1940! Oh, well, what's 35 years here or there?
The date appears to be incorrect on this bridge. It is on concrete abutments, which would make post-1900. The lateral struts look similar to those on some Vincennes Bridge Company spans.
Not to mention all of those derelict spans sitting out there in the weeds that have fallen off of the county or state inventories, sometimes as much as 50-75 years ago. I have had luck with comissioner's minutes from long ago, but it is a tedious and time consuming process. Unfortunately, in many instances these records have been lost.