IE6 is not supported by dolphin, and IE7 is not much better in the respect that it has some major flaws in DOM rendering.
Users of IE6 + 7 will experience similar issues on other sites - this is not just limited to Dolphin.
There is a built in warning message that tells users of IE6 to upgrade (IMHO this should be expanded to include IE7) - there really is no reason to support IE6 unless you are serving Dolphin on an intranet where there is a captive audience of IE6 users with no option to upgrade due to administrate restrictions. Even Microsoft themselves agree on this point - I blogged about this recently - http://www.deeemm.com/news/145-its-official-ie6-is-outdated.html
IE8 should however be fine.
There is a javascript library that you can use that MAY help some issues - it is supposed to address various IE DOM interpretation issues - this can be found here - http://code.google.com/p/ie7-js/
I have found that the one of the causes of the issue I have found, is that some libraries are not loaded in time causing the dependencies to flag an error and fall over - a quick fix is moving the problem javascript calls into the body of the document, or sometimes to the bottom of the document - thus delaying their operation. Additionally, issues can also be caused by conflicts between javascript libraries.
This is obviously little more than a quick hack, and the ideal solution is to isolate the cause, which involves analysing each individual error and remedying them one by one.
Probably not the answer you want to hear, but a general question deserves a general answer.
HTH
/DM