[SalesForce] No log for Visualforce errors

First off, to debug this, I would take the VisualForce page out of the equation. That's what unit tests are for. Create a test class that inserts the necessary records (Accounts, Package information records...), exercises your controller and asserts that the tasks are created. Once you know your controller logic is working, creating the VF page is just markup and data binding.

I would also remove some code that, in my opinion, is a bit redundant and just complicates reading the code. Apologies if I sound pedantic (that is not my intention), but in the past I've seen many times how cleaning up your code makes bugs in the code more obvious to see.

For instance, you have a catch block that returns null, when the normal method exit point returns null. You instantiate a standard controller just to save a record... can't that be done with a simple update statement? Your saveChanges method could look like this:

public ApexPages.PageReference saveChanges(){
    for (Package_Information__c packs : accountPackages){
          try {
            sendTask();
            update packs;
          }
          catch(Exception e) {}
    }
    return null;
}

Incidentally, it might be worth adding a debug statement in that catch. Perhaps your code is ending there?

If you do this with all your code, there's fewer lines of code and fewer things to go wrong.

Having said that, my guess is that accountPackages.equals(accountPackagesClone) is evaluating to true and you're exit the statement. Is that funny debug statement (as highlighted by @brovasi) supposed to be the indicator that 'The clone equals the original'?

This is one confusing area of Debug Log: you always need to set it on a User because class/trigger debug flags don't actually generate logs.

Setting class and trigger trace flags doesn’t cause logs to be generated or saved. Class and trigger trace flags override other logging levels, including logging levels set by user trace flags, but they don’t cause logging to occur

See documentation