Ok. I'm new to this site, and to my Mazda so bear with me!

I inherited this 06 Mazda3i 2.0 with a lot of issues, and so I've been working to get them all cleared up. Before I began this process, the car was running extremely rough. It seemed like you had to shift very early because the RPMs were very high at very low speeds. It was also vibrating/shaking like crazy especially when you accelerated. The car was also super loud, it sounded like the car had a fancy intake or sport muffler, but it did not. To fix these issues, so far, I've:

1) replaced all the spark plugs with the OEM iridium plugs Mazda recommends.
2) oil change / replaced the air filter (it was like it had never been replaced ever... yuck..)
3) put on a new muffler - nothing fancy, the old one was bent up under the car right next to the gas tank and seriously had to be replaced.
4) replaced the engine mount that is right next to the transmission (not sure what # that one is...)
5) replaced a broken ball joint and gave the car a much needed alignment

The car is running soooo much better, HOWEVER the super loud sound has not gone away. Its only when you accelerate, doesn't happen in neutral and/or when your not pressing the gas... It literally sounds like the car has a fancy intake, but everything in the intake is stock. I thought this sound was being caused by the bad muffler, but it's still there after replacing it. The car still also vibrates ever so slightly, but not nearly as bad as it was. Here are my concerns, could it be:
a) broken CV shaft from the bad motor mount? Would that cause the engine to run loud (I don't think so.. but it might cause the vibration?)
b) The vibration from the bad motor mount did tear the intake duct. I have one on order, but in the mean time I patched it pretty awesomely with electrical tape. Could this cause the sound? If so, how come there was no reduction in sound after patching it...

Has anyone had this issue? Does anyone have any idea as to what it might be?
PLEASE HELP!!! THANKS!!!!!!!!

 

If you managed to break the transmission mount then I'd definitely suggest you check the passenger side mount as it's one of the most common things to break on this car. If that's broken it could be contributing to vibration. Likewise if you have a problem with a CV joint it could cause a vibration at speed.... check the boots and see if there's any sign of them being broken.

You said you had the alignment, but have you checked the tires themselves? The 3 eats tires if they aren't rotated frequently and it certainly seems like the car didn't have proper maintenance before now.

As far as a clear engine noise when you accelerate.... have you checked to make sure you don't have any exhaust leaks or cracks? Does it get any better once the car has heated up to operating temperature or does it remain?