You should be able to shift at any RPM up to redline in each gear without any grinding.
With that said, there could be any number of issues causing the symptoms that you describe.
Be sure that you're getting the clutch all of the way in and not hammering the gear shift. But you shouldn't have to baby it or shift extra slowly either.
With that being said, it sounds like your 3rd gear synchro is being problematic.
Start with the three items that Crooster mentioned: Check your front motor mount, check the clutch hydraulics, and change the transaxle oil (using the expensive factory oil for the refill). The only other thing I would add is to have your mechanic check the shift cable adjustment.
If nothing comes up amiss, then its most likely the synchro. You can either pull the trans and have it repaired or swap in a used trans.
It is generally cheaper to swap in a replacement as they are typically available for around $500 and the parts + labor to repair your existing trans is likely to be more than that. (
00 01 02 03 04 Porsche Boxster 2 7L 2 7 5 Speed Manual Transmission 19 037 Miles | eBay
I had the exact same problem with my 3rd gear synchro and swapped the trans myself after buying a used trans from another member here on the Forum. Should take a typical DIY'er 8-10 hours. Its not technically difficult but rather just a lot of stuff to remove and re-install.
Good luck and let us know what you find.