For users who want to use Falcon Pro again, get the update here it is now officially free for all). Install it. Then do the steps below to be able to use it. (If you already had a token/were authorized before Twitter cut it off, you wont have to do any of the things listed below. Itll just update the app. Thats what it did for me at least.)
On your device or computer:
1. Visit
https://dev.twitter.com and sign in (it doesnt matter what account you use for this step)
2. Click on the My applications link in the dropdown under your picture.
3. Click on Create a new application
4. Fill in a unique name (you may have to try a few names before you get one that hasnt been claimed), a description, and URLs for the Website and Callback. It doesnt matter what URL you are using, but it must be correctly formed (
http://something.com).
5. Check the box to agree to the Developer Rules Of The Road, fill out the captcha, and click the button to finish.
6. Click on the Settings tab and change the Application Type to Read, Write and Access direct messages, then click the Update button at the bottom of the page.
7. Switch back to the Details tab and copy the values for Consumer key and Consumer secret.
In Falcon Pro:
1. Go to the login screen (logout if youre logged in)
2. Tap all four corners to light up the squares (see screenshots), then tap the orange one (bottom left) to turn it back off.
3. Shake your phone/tablet. Yes, really, start shaking it until a dialog box pops up saying Custom login unlocked!
4. Tap on Custom login
5. Fill in Consumer Key and Consumer Secret with the values you got from creating your Twitter APIkey. These are long, case-sensitive strings, so be careful to copy them precisely.
Hope this helps some of you out. Especially the people asking about Twitter apps to use now that Falcon Pro was out of the game. All updates will be handled through the link above from now on, it will be updated outside the Play Store.
EDIT: Link for download fixed/corrected.