Is there some module which detects untranslated strings?
To my knowledge, the answer to your question is = No there is no such module. Checkout the article Drupal's multilingual problem - why t() is the wrong answer to beter understand the various challenges to be addressed with anything related to the t() function ...

Drupal's translation system consists of 2 basic components: the translation of the interface and the translation of the content of a site.

The translation of the interface is about the translation of various text strings used throughout the site, like labels used on buttons such as submit, or on tabs such as view or edit. They are the same on all sites (no matter what actual content is contained in a site). This is also what the t() function is related to.

The translation of the content is about the translation of nodes and entities. It requires a place to actually store the translated versions of the content (in multiple languages) and a system to choose which content is to be displayed where. The systems available for translation of content are:


Content translation (used in earlier versions of Drupal, and still available in D7), which translates entire nodes in multiple languages.
Entity translation (its API was first introduced in Drupal version 7, though there is no UI for it yet), which translates fields attached to the same entity.


Typical (often used) modules (in D7) related to translation of the interface (apart from the i18n module of course):


Variable.
Localization update.
Entity Translation.


For D7 there are basically 2 alternatives available to facilitate the "management" of translation of content:


Translation Overview, mentioned as a recommended add-on on the i18n project page also. From its project page:


  ... provides a table listing the site's nodes and showing what's been translated into each language. It also lets you assign priorities for translating nodes into the various languages.

Translation Management Tool, considered as the successor of the previous module, and "the" module to move forward with in D8 also. From its project page:


  ... provides a tool set for translating content from different sources. The translation can be done by people or translation services of all kinds. It builds on and uses existing language tools and data structures in Drupal and can be used in automated workflow scenarios.
  
  This module does not make i18n or any other language module for Drupal obsolete. It does only facilitate the translation process.



PS: Obviously, translation of content is NOT what this question is about (at least not yet ...), but pretty sure a related challenge you 'will be' (or 'are already'?) facing in this multi-lingual site ... and which cannot be handled with the t() function. Though for the sake of completeness, I hope it's OK to add that part of my answer also ....