Platform:
Windows 7

ISP:
Comcast

Type of Internet Connection:
DSL

Internet Connection Speed:
2MBit/s

Date & Time:
I'm not sure of the exact time frames for each occurrence of the top of my head.

Frequency:
Always.
I haven't failed to reproduce it while actively trying.

Physical Level:
50

Area and Coordinates:
Again, I am not certain. I was able to reproduce it on the ferry ride between Limsa-lominsa and Thanalan, as well as in numerous areas of Thanalan. I have had friends confirm with me they have been able to reproduce it wherever it is attempted, even inside the new instanced raid dungeons.

Party or Solo:
I was solo. It has been done in a party as well, though.

Steps:
I'm not certain how it was originally discovered, as a friend simply told me about it. I decided to see if it were true, and I succeeded in reproducing it multiple times. Gear did not seem to matter, as I was able to reproduce it regardless of what equipment I had on at the time. I can confirm that it did work with the following setup, though again it did not seem to matter.

Aeolian Scimitar
Decorated Iron Scutum
Templar's Chain Coif
Templar's Haubergeon
Iron Gauntlets
Iron Sabatons
Iron Plate Belt
Garnet Ring x3

I was able to reproduce it by simply activating the buff while in passive or active mode. Then by running forward and repeatedly entering and exiting active mode by pressing the F key as quickly as possible (As to keep the queries to the server for that command back to back, I suppose) the Quickstride movement buff is able to be kept on for an indefinite amount of time. The buff does tick down to 0:00 seconds, but once it reaches zero it simply stays at 0:00 so long as you are constantly entering and exiting active mode. If there is a delay in either entering or exiting active mode, the debuff will wear off and you lose the quickened state.

I was not using any macros, and there were no error messages.

I hope that is detailed enough. If not, I'll do my best to get in game again soon and reproduce the events again with multiple gear set ups and locations.