Tips for multiple-pronunciation characters (多音字) This is a broad request for tips, but I have a specific question in mind as well.

尽 can be pronounced as "jin4" or "jin3".

In Pleco, the definition for "jin3" is "to the greatest extent" while one of the definitions of "jin4" is "to the utmost; to the limit".

Perhaps this is a translation issue, because to me, these 2 definitions are essentially the same. Based on this, I still have no way of knowing when the character is jin4 or jin3 when it means "to the utmost" or "to the greatest extent".

Is this just a brute force memorization problem or are there some tips for figuring out when to pronounce it one way &amp; when to pronounce it another?
To answer your specific question, it should be kept in mind that 尽 is a simplified character that merged both traditional characters 盡 (jìn) and 儘 (jǐn), which is why it appears to be a 多音字 in Simplified Chinese.  The difference between 盡 and 儘 is very subtle though.  This link talks about the difference as it applies in Cantonese, but I believe it applies in Mandarin as well:


  「儘」是「力求達到最大限度」，強調的是「力求」，至於能否達到「所求」，不得而知。「盡」則有「達到最大限度」的意思，強調達到。
  
  儘 is "strive to attain maximization", with the emphasis on "strive"; whether it can be attained is unknown.
  盡 on the other hand has the meaning "attain maximization", with the emphasis on attaining.