How to do mass payouts in my application to multiple addresses at once, or very quickly?
In Electrum you can use the CSV import feature to make bulk payments. It can accept either a CSV file or CSV entered into a text box. The rough format is:

ADDRESS, 0.12345
ADDRESS, 0.12314


This feature has been merged into the 1.9 version that is not released yet, but you can use it already.

https://github.com/spesmilo/electrum/pull/282

Example:

1PkeTTctdh2CvhW3fQLs93PWP9qupWV68X, 5
3NujXLC3LxNsmk2wr69CLBuXGfhXeenUyu, 5
1CNAnSb7d1XCA4AXBH2gip3mi8dNTQxzeo, 1
1LSBFJ1An9orRMU6Bz3NS1y3jr1eH9AexE, 1
16qRyDVZVpptJb4HZzv5rWkjqtJWVRjDep, 1
1PkeTTctdh2CvhW3fQLs93PWP9qupWV68X, 5
1Nnad832Zyob64wGbju49CC5RFbACAfCNZ, 1
1J2gFYBnf8K2wHJDndgr3iN1nPoZumHXap, 5


The amount is in the unit your Electrum is configured. In my case, for example, it is in mBTC. Be careful with this!