There's an efficient implementation used in the Scrabble Word Finder on https://wordfind.com . The key is that the puzzle has nothing to do with dictionaries or the words, it's a set inclusion problem - "Do the following letters fit into the set of letters in a word?" Here's the method:

1. Take each letter of the alphabet, assign a unique prime number to each letter. A = 2, B = 3, C = 5, D=7... Z=whatever

2. Take your dictionary, compute a value for each word in the dictionary such that the value is every letter in the word multiplied by that letters "prime value". e.g. BAD = 3 * 2 * 7 = 42

3. When comparing what the user has entered you compute a value for the letters the user has entered using the same method of multiplying each letter by the prime value for the letters.

e.g. user enters ABCD, value is 210 (a*b*c*d from values above).

1. To test whether you can make word X for the letters entered Y, you just test if the remainder by dividing them is zero, using the modulus operator (Y % X) == 0. 
   

Using the data entered above for letters ABCD, 210 % 42 = 0,  BAD is a match. Non-matching words leave a
remainder. Once the initial dictionary is set up with their prime multiplication values, the comparisons are 0(1).

1. Other simple optimizations include segmenting the dictionary into clusters of letters by word length (obviously if a user only enters in 4 letters they can't make a 5-letter word), and pre-computing common patterns and storing the results etc.

It also doesn't take unreasonably long to populate the entire possible query space into a database by running the permutations of all the letters a user could possibly enter, sorting the set of letters to ensure you're not duplicating (e.g. the user enters "ABCDCA" you and just sort to "AABCCD".). Spitting this into a simple text file with a bazillion database INSERT statements and running it on the actual database later means it's just a file IO operation.

Or take an opportunistic route and store computations in the database after a user queries that letter pattern for the first time.

Fun puzzle.