Let me first say, that I consider links to papers referenced in MO posts a useful things. And so do other users, judging by an older discussion on this topic: Is it worth editing old posts to add links for references?
Occasionally you can find links which contain part related to proxy of a specific university. I mean links such as
http://jlms.oxfordjournals.org.proxy.lib.umich.edu/content/s2-15/1/134 (from this answer) or
http://www.jstor.org.proxy.lib.umich.edu/stable/2372821 (from this answer), etc. Links like this have been briefly discussed also in comments to this question: edits with links to material under restricted access.
As far as I can tell, links like this only work for somebody who accesses the material from the network of particular university or if you have password for this specific proxy. (Correct me if I am wrong.) And since the link works fine on the OP's end, the OP might easily miss that there might be a problem for others.
Such links are rather easy to correct. And I edit such links when I spot them. (This basically amounts to correcting a "broken" link, which I consider an improvement of a post.) Usually all you do is to omit the part which contains the university proxy and you get a working link. (Like http://jlms.oxfordjournals.org/content/s2-15/1/134 and http://www.jstor.org/stable/2372821 for the two examples mentioned above.) Even if my institution does not have access to the particular journal or issue, I can still check that the link works - it gets me to the paper referenced in the post.
However sometimes you can see links to MathSciNet searches in posts. (Which are probably useful - otherwise the OP would not include them - although they are probably only useful for users with access to MathSciNet.) As an example, I can mention this link: http://www.ams.org.ezlibproxy1.ntu.edu.sg/mathscinet/search/publdoc.html?arg3=&co4=AND&co5=AND&co6=AND&co7=AND&dr=all&pg4=AUCN&pg5=TI&pg6=PC&pg7=ALLF&pg8=ET&review_format=html&s4=Habiro&s5=claspers&s6=&s7=&s8=All&vfpref=html&yearRangeFirst=&yearRangeSecond=&yrop=eq&r=2&mx-pid=1735632 it is used in this answer. A natural guess is that link should work after removing the
ezlibproxy1.ntu.edu.sg part to get http://www.ams.org/mathscinet/search/publdoc.html?arg3=&co4=AND&co5=AND&co6=AND&co7=AND&dr=all&pg4=AUCN&pg5=TI&pg6=PC&pg7=ALLF&pg8=ET&review_format=html&s4=Habiro&s5=claspers&s6=&s7=&s8=All&vfpref=html&yearRangeFirst=&yearRangeSecond=&yrop=eq&r=2&mx-pid=1735632. However I cannot test whether the link indeed is correct, since I only get to the box saying that "http://www.ams.org/ requires username and a password".
Is it reliable to change links in this way? Should I expect that somebody with MathSciNet access will check the link if I am unable to? Should I explicitly ask somewhere (perhaps in chat) whether somebody would be willing to check the link?
Of course, I am aware that this is a very minor problem. (And I do not expect that there will be too many posts like this. If I try to search for url:*mathscinet*search*) I only get 251 posts. And I assume that the majority of the posts contain working links. If I try url:*proxy*mathscinet*search* or url:*lib*mathscinet*search*, I only get 4 posts - but perhaps that are other strings used in similar links.)