2002 wrx auto problems
I recently bought a 2002 wrx auto used with 143,000 miles on the clock. It has an automatic transmission. It has a couple odd issues that have been confounding anyone I have take a look at them other than to recommend a new transmission. Given the cost of a replacement I hope it is something simpler. Since owning it I have done an oil change, full transmission flush and filter change, and put in a new battery since the old one was giving out on me. The issues are as follows
1. speedometer reads 10 to 20 mph over actual speed based on how fast I'm going. Has been a consistent issue since I bought the car, but not mentioned by previous owner.
2. Downshifts hard from 4th to 3rd when you punch it. If you press lightly till it shifts, then hit it, works fine. This issue was mentioned by previous owner as existing since the car was much newer. Subaru apparently had no explanation for this, other than putting in a whole new transmission in. this is not a huge issue for me, but including for diagnostic info.
3. Car shudders/takes a while to go from 1st to second. This issue varies somewhat randomly. It was much better after I replaced my battery, but got worse after, and slightly better after doing full transmission flush.
Any thoughts are appreciated