Users with at least 2500 rep and an answer score of 5 in a tag can suggest synonyms for that tag. (Details can be found, for example, in this meta question.) Hypothetically, it is possible that 5 users vote on a synonym before anybody notices them and in this way some synonyms which are "problematic" might be created. (By "problematic" I mean synonyms which are against consensus reached in previous discussions on meta or synonyms which many users would consider undesirable but did not notice that they were suggested.)
To list some examples from the past, at some point the synonym (summation) $\to$ (sequences-and-series) was suggested, despite the fact that summation tag was created explicitly for finite and formal sums (and this is also explicitly mentioned in the tag-info) - "summation" tag for finite and formal summations. (In fact, several users devoted quite a bit of work to retag some questions asked before (summation) tag was created.) There was also synonym suggestion (discrete-mathematics) $\to$ (combinatorics), which was discussed in this meta question: Do we really want (discrete-mathematics) $\to$ (combinatorics) synonym?
- Is there some easier method to monitor new suggestions for tag synonyms other than frequently checking list of tag synonyms? (For example, a feed which could be directed into chat room and would list new synonyms and synonym suggestions.)
If some tag synonym gets approved but it is considered wrong, is there some other way to repair it other then retag all questions manually. (For example, would it be possible at least to get back tags from the time of the last data dump in SEDE?)(Removed based on quid's comment - since this part actually does not make sense.)
Just to clarify, I am not against creating some tag synonyms if it is generally approved by the community. (For example, if the position on my two examples above changes, they should be synonymized.) This is only about the possibility that some "incorrect" synonyms might be created without being noticed. (I cannot be sure about that, but I do not think that there are many users who regularly visit the list of tags synonyms to see which new synonyms have been created.)