Yankeeboy515

This is because the API was introduced in 0.2, so it wont work with anything less and I keep the older versions of my mod up.
For accurate versions see the file name, it says "LSPDFR 0.2a and RPH 0.20" for the latest version as that is what was used. I'll always do this to help people with compatability problems.

Since it's a shortcut it's not needed. delete it. (after doing that, try the game. that could be the problem). Also the callouts/plugins you have, are they the up to date versions? 

Ok a new version to Strays Callouts were released yesterday so you should update it. Once it's downloaded, remove CalloutsV, install Strays Callouts and test it out and see if it crashes.
Then take out Strays Callouts and add CalloutsV and then test (essentially trying them seperate) if no crashing occurs try them together and see if it works. 
Also what version of CalloutsV are you using? 

Just in case, i'd re-download CalloutsV, They get updated a lot so it's hard to keep track of what is updated =/

This is why we have changelogs :P
Your problem lies with the following line:
[7/23/2015 4:11:20 PM.550] LSPD First Response: Exception message: Method not found: 'Void LSPD_First_Response.Mod.API.Functions.PlayScannerAudioUsingPosition(System.String, Rage.Vector3)'.
This is a new method that allows us to play scanner audio, your LSPDFR version is 0.2 RC7 which DOES NOT include that method above. you need to update your LSPDFR to 0.2a

He does have 0.2a.. Wait, no. you're right 0.2 RC 7.
@Yankeeboy515 you'll need to upgrade to 0.2a for plugins to work. 

Ok so after look through your log it's an issue with your plugins, are they blocked by any chance? Right click on the .dll and .ini files - click on properties and at the bottom does it have a button that says "Unblock" like in the screenshot? Also, may i ask what the Police Scanner shortcut is in your screenshot? 

To find the log for rage hook
go to RagePluginHook.ini   (THE LOG IS FOUND RIGHT UNDERNEATH THE LAUNCH APPLICATION) it will have a little picture that has a piece of paper with a gear on it. Open that... Copy its contents and paste them here!