I. Preliminary Remark
There are a couple of problems one can encounter when installing, reinstalling or moving a WordPress blog. I have documented some I have met here and in a follow-up article here in German.
But as I had drafted some aspects of the second article in English, too, I will publish them here also in English. The German articles are much more extensive, though, and I suggest rather reading them.
II. Problems and Solutions
1. Strange Signs, Strange Words, Strange Numbers at the end of my URLs
1. E.g. “#.”, followed by other signs
The solution lies in disabling the track address bar shares-function of AddThis, cf. here.
2. E. g. ?doing_wp_cron=1351935560.6119229793548583984375
The reason is described here: http://wordpress.org/support/topic/doing_wp_cron or here: http://wordpress.stackexchange.com/questions/12777/what-is-this-doing-wp-cron. Also see http://wordpress.org/support/topic/scheduled-posts-still-not-working-in-282?replies=13.
I thought it had vanished (in my case) after disabling Wassup, which was obviously running a lot of cronjobs.
But the phenomenon occurred again when I used Ajax Edit Comments, persisting while someone had posted a comment during the period in which it could be edited. That would mean if you have a lot of commentators, that might show a lot on that post. It may have been a coincidence, though as It may also occur with other plugins, see e.g. here.
So I had to speak to my web host, but loopbacks is enabled.
Finally, I found out here, that, although I could not find a trace of ALTERNATE_WP_CRON n the wp-config.php, it was set in the code-pages of the plugin. Apparently, the All in One Event Calendar plugin defines ALTERNATE_WP_CRON in a place I did not expect it to be. So I add to my wp-config.php the following line:
define(‘ALTERNATE_WP_CRON’, false);
And the URLs look nice and clean again . 
2. Visual Editor and Ultimate TinyMCE and TinyMCE Advanced Editors not showing
Although I activated Ultimate TinyMCE and then TinyMCE Advanced, I got no more buttons, nor (as I realised when comparing with my old setup) the visual editor.
I could resolve the latter by enabling again the visual editor in the user preferences (I might not have gotten there without a chain of hints here and here, then I would also have found the solution here).
3. Ultimate TinyMCE-bar “too wide”?
Just change the number of rows or open your browser wider (I really did not realise I could do that… done too much on the net, then?) – or choose the 1-column-view in WP (slider on top of the page). You could also add rows in the code, maybe.
4. Page Title Doubled
I checkmarked “fin Yoast. For quite a different advice see http://en.forums.wordpress.com/topic/dont-show-page-title-in-page-body?replies=9#post-606411, http://www.prasannasp.net/fix-seo-by-yoast-prints-site-title-twice, http://wordpress.org/support/topic/site-title-showing-double, http://voodoopress.com/modify-header-php-to-get-the-most-out-of-yoasts-seo-plugin-in-a-twentyten-child-theme.
5. AddToAny-Button on Search Results Page doubled
I am still looking for a solution. I hope that someone will reply here.