Make sure the cucumbers are firm and fresh and free of blemishes. Cut 1/16" off the blossom end.
As Tracy said, the vinegar/water ration should be at least 50/50. Official word;
"Caution: The level of acidity in a pickled product is as important to its safety as it is to taste and texture.
Do not alter vinegar, food, or water proportions in a recipe or use a vinegar with unknown acidity.
Use only recipes with tested proportions of ingredients. There must be a minimum, uniform level of acid throughout the mixed product to prevent the growth of botulinum bacteria."
That's not written to be lawyer proof - it comes from laboratory testing to see what is needed to prevent the bacteria growth. You'll have a better product that you won't have to throw out if it is spoiled. To each their own.
Firming Agents - "Alum does not improve the firmness of quick-process pickles. The calcium in lime definitely improves pickle firmness. Food-grade lime may be used as a lime-water solution for soaking fresh cucumbers 12 to 24 hours before pickling them. Excess lime absorbed by the cucumbers must be removed to make safe pickles. To remove excess lime, drain the lime-water solution, rinse, and then resoak the cucumbers in fresh water for 1 hour. Repeat the rinsing and soaking steps two more times."
I personally wouldn't go through all that trouble...I'd use the Pickle Crisp which is calcium chloride.
"To further improve pickle firmness, you may process cucumber pickles for 30 minutes in water at 180°F. This process also prevents spoilage, but the water temperature should not fall below 180°F. Use a candy or jelly thermometer to check the water temperature."
This is called the pasteurization method. I used it last year and liked how my dills came out.
Here's a pickle problem sheet. For soft pickles, it lists vinegar too weak, not enough brine, not processed to kill enzymes/microorganisms, moldy spices, blossom end not removed.
http://nchfp.uga.edu/how/can_06/pickleproblems.html
I checked the nchfp dill recipe. It is somewhat similar to yours. The vinegar is not 50/50 - 1 1/2 qts vinegar to 2 qts of water, with 1/2 cup of salt. You can take a look here.
http://nchfp.uga.edu/how/can_06/quick_dill_pickles.html