Check whether letters of word are in alphabetical order
CJam, 8 bytes

lel_$_&amp;=


Here is a test harness for all examples in the challenge. This returns 0 or 1 (which are falsy and truthy, respectively, in CJam).

And here is a script to filter the word list in the question (takes a few seconds to run). You'll have to copy the word list into the input field manually, because it's too long for a permalink.

Explanation

l        "Read input.";
 el      "Convert to lower case.";
   _$    "Get a copy and sort it.";
     _&amp;  "Remove duplicates (by computing the set intersection with itself).";
       = "Check for equality with original (lower case) word.";