Issues with drop down menus:

• long text can make the menu unreasonably wide;
• difficult to access the options in a text-only/speech browser or through keyboard navigation;
• hard to quickly scan the list for a particular option;
• some users may not be aware there are more choices;
• drop-downs can be tricky for some users to use (“I didn't know you had to press ‘Submit’”);
• display differs depending on platform/browser;
• an, though minor, they rely on some programming (either back-end or client-side) to work.

For some additional comments read what the still relevant Macintosh Human Interface Guidelines has to say about it calls “pop-up menus.”