Many details have changed related to themes, between Tikiwiki 2 and 3, so there could be problems for sites that are using customized themes, or themes that are no longer part of the Tikiwiki package.
Big changes in default template (.tpl) files
In Tiki 3, the page layout method for the left, center and right columns uses floated divs, rather than an HTML table. In Tiki 2, several themes used this new method, but they had their own tiki.tpl, etc. Now this method is the default, and there are no more themes in the package that use the old table-based method.
This means that any theme at a site that previously depended on the old default templates will have broken column placement in Tiki 3 (all columns will be full page width, with the center column first, followed by left and right columns).
The page-top "site identity" area has been changed radically. Previously, Site Identity was an optional feature. Now there is no permission check for Site Identity, which was redundant since there are checks for each of the components within Site Identity. Old templates that have a Site Identity permission check won't display the contents anymore. The contents, arrangement, and location of Site Identity have changed also.
Many small details of the template files and stylesheets have been changed. Examples include buttons, search forms, menus (PHP Layers but especially suckerfish (CSS menus)). Also there's been a lot of simplification of selectors in order to have more consistency across features — i.e., making comment posts the same for forums, page comments, blog posts, for example. This means that old stylesheets will have many mismatches when trying to work with the new templates.
Re-implement using a Tiki 3-compatible stylesheet
Old Tiki layouts that are the full width of the page and liquid, with no empty side-margin areas, can use the default tiki.tpl, so won't need their own template. A stylesheet alone is probably all that will be needed for the theme. But it will be necessarily to create a Tiki 3-compatible stylesheet that achieves the old look of the theme. I suggest using one of the theme stylesheets in the Tiki 3 package as a starting point, renaming it, and modifying it to achieve the old look.
But an even better solution would be to use a new feature of Tiki 3 called the theme option. When selecting a theme on Tiki 3's Look and Feel admin page or in theme-switching module, sometimes there is a second select dropdown list (such as with the Strasa or The News themes). This extra dropdown list will activate a second CSS file that appends the styling of the main one.
Site admins who want to "customize" an existing theme can now do this easily by making a small CSS file that overrides or adds properties to the primary theme. This way, in site upgrades, the main CSS file (if it is a bundled theme) will get updated, but the theme option file won't be touched, so will continue to adds its extra styling.
To use this method, in the styles/ directory, to add a new option for, e.g., the Feb12 theme, a new directory would be added like styles/feb12/options/. Then the new theme option file would be put in this options directory. If the theme option (called "green" for example) uses images, these images would go in a styles/feb12/options/green/ directory. Check the styles/strasa directory for an example of the necessary arrangment.
Specifically, what CSS selectors no longer work, and what has replaced them? I hope to list these sometime soon. In the meantime, pointing FireFox and the Firebug add-on at a page is a great way to find out what CSS stylesheets, selectors and properties are being used for any item on the page. themes.tikiwiki.org is still running Tiki 2 and demoing older themes, so can be used as a reference for sites that have already upgraded to Tiki 3 and need to check the old layouts.