Pulsars and neutron stars/Mistakes and red herrings in pulsar research
Reading the history of pulsar research may give the impression that progress is made in an orderly manner. Of course, this is not always the case. Even the first pulsar was serendipitously discovered. Pulsar data sets are complex and often the initial results are not clear or are confusing. Single bursts in the data set can have an astrophysical source (possibly even from distance Galaxies) and yet other bursts (with quite similar, but not identical, characteristics) can come from a microwave oven (Burke-Spolaor et al. 2011).
Methods can be correct, but slight errors in the implementation can lead to significant confusion. The first proposed extra-Solar planet (Bailes, Lyne & Shemar 1991) turned out to be an error in accounting for the Earth's motion around the Sun. The first actual extra-Solar planet is true, but many people considered other possible explanations such as phenomena in the heliosphere .
The hunt for a pulsar in the supernova SN1987A continues. An optical detection was reported by Middleditch et al. (1989). This was followed up later by  where it was stated "we believe the observed signal is electrical noise from the closed-circuit television camera used for acquisition .... All this was undoubtedly a combination of bad luck (or divine malice), misplaced pattern-finding skills, and the common human tendancy to overinterpret a limited amount of data".
The pulsar literature is full of interesting (and erroneous) discoveries and interpretations: the Crab pulsar was considered to be in a binary system, the first report of a direct detection of gravitational waves using pulsars (), the first pulsars "discovered" in the 47 Tucanae globular clusters and many, many more.