Calendar widget translate problem on Drupal 7
If you by date widget means the JS popup, then that part is not actually translatable in Drupal. Instead you need to activate a load a language js file for the jQuery plugin which will translate the widget for you. If those translations are wrong, you should file a bug report with the jQuery team.

I searched the data module and couldn't find the text strings that you mention above. Drupal 7 allows modules when creating translatable strings to provide a context. I see that the date module does that several places:

t($date-&gt;format('F'), array(), array('context' =&gt; 'Long month name', 'langcode' =&gt; $langcode));


Doing this will create an extra translatable strings. An example use would be:

t('Order', array('context' =&gt; 'the order of items');
t('Order', array('context' =&gt; 'an e-commerce order');


The word is the same but the meaning is different, by doing the above it will allow translators to translate the strings differently. If a Drupal module provides the text strings for your widget, they will need to do something similar: fx

 t('T', array('context' =&gt; 'Tuesday');
 t('T', array('context' =&gt; 'Thursday');


If the module haven't done this, your best bet is to submit a patch for the module and explain why they need to do this. This is generally a good practice to do when you create translatable string that aren't unique.