link farm refers to a page having links of too many pointing unrelated sites... maybe it depends on volume and relevancy of links btw, i heard a news before... that ajax could weaken web 2.0? http://www.informationweek.com/showArticle.jhtml?articleID=201202520&cid=Answers
I heard rumours that googlebot doesnt read ajax properly, since all contents are hidden behind JS and there is no static HTML. However i dont know what could be the outcome of this, since googlebot might feel that u r trying to hide something behind the Ajax interface. Mostly companies use ajax behind login pages, so they are least bothered about SEO etc on internal pages, in fact they dont want login pages to be spidered. Wondering why you wanna do this? Trying to hide external links? However from a content perspective, i am not sure about this.
Pretty sure that ajax masks links and they don't get crawled by google. Ajax is currently not seo friendly. As ajax grows more and more popular it may be fixed and crawlable in the future which would be awesome cuz ajax is bad ace.
Well, it depends on your way of using AJAX control and update panels if you can export all the results in HTML code format then you will have no problem with search engines after all.