From the implementation of the Hardwicke Act in 1754 the marriage register includes the names and signatures (or marks) of the witnesses. In many cases these would have been relatives of the bride or groom - often siblings or parents.. In cases where there may be problems of identity (see Right Name Wrong Body) looking at the register entries of all relevant marriages and matching up names can be very useful. For instance, by comparing the signature of a witness at a wedding with the bride at another could help to decide whether they were one and the same person. While many people who could not write simply made a cross as their mark, some people had a distinctive mark - so this is worth checking as well. In doing this female witnesses who sign the register after they had married and changed their surname are particularly helpful..
It is important to realise that when a couple were married in church from July 1837 onwards, they signed in the church register. The civil copies - which you get from the local registrar or through the GRO - are copies made by clerks. This means that the signatures on a marriage certificate from the microfilm of the church marriage register can be used for identification - in the same way as signatures are now used on bank cards, etc.
When you are looking at a marriage register it is always worth looking at the other entries. Sometimes a church warden would witness a fair percentage of marriages - and a glance at the register could show that your "mysterious" witness had also witnessed many other marriages so was probably not a relative. In addition witnesses are not indexed on the IGI and many other indexes and a scan for the surnames you are interested in among the witnesses could suggest new surnames which may be related.