Not sure what you mean exactly but if the structure on two sides of a bridge are sufficiently different would you want to drive over the bridge. Best wishes David Booth
A plot of the data will reveal any significant breaks or discontinuity. One good example of breaks is that during war years consumption might break off from its normal trends. Some analysts would throw away such breaks in the data to maintain normality.
Another case is that you may know when a new method, a new technology is implemented over an old one so you may want to check for the difference. Yet another case in Global analysis is where countries use different classifications of their industry data. In the case of US-Mexico-Canada FTA, industries moved away from SIC classification to NAICS. So, in these and similar cases you should check for breaks.
Incidentally, breaks such as caused by re-benchmarking of data can be accommodated by using a consistent benchmark date of the data. I mention this because the US Census (BEA) practice re-benchmarking of data such a employment and labor force statistics..
Its depend on the problem under investigation, however, I think it is important to test for structural breaks. At least it can help to understand the data.
One of the way is by plotting the data to look for breaks. Structural break is basically when time series abruptly changes at a point in time. For instance, in economics, we are aware that most of the macro variables(eg GDP growth in India) will show structural break due to certain economic events like economic liberalization, Global financial Crisis etc... So, I think if we take into account structural breaks, the findings are more reliable.