If it works when you slow things down with alerts, it looks like you may
actually want an SJAX (!) call--I mean, if this page is pounding the browser
with tons of AJAX threads, maybe you only want to do one at a
time--Synchronously.

so, instead of:
$.getJSON("http://library.paulsmiths.edu/issnsearch/ispeerreviewed.php?i
ssn=" + issn + "&jsoncallback=?",function(json, textStatus) {
                                alert("test2");
                                allHTMLTags[i].innerHTML= "(" + issn +
") Peer Reviewed: " + json.peerreviewed;
                        });

maybe something like:

$.ajax({
  type: "GET",
  async: false,
  url: "http://library.paulsmiths.edu/issnsearch/ispeerreviewed.php?issn=" +
issn,
  dataType: "jsonp",
  success: function(json, textStatus) {
                                alert("test2");
                                allHTMLTags[i].innerHTML= "(" + issn +
") Peer Reviewed: " + json.peerreviewed;
                        }
});


Also, I agree with what other folks said about using as much jQuery as possible.

Jason