After looking high and low for a decent car under $5,000, I finally purchased a 2003 Infiniti I35 with 130,000 miles on it. I wanted something more exciting, but beggars can't be choosers when you only have $5k to spend. It has been taken care of very well by its two previous owners. Only problems with it I need address are an uncomfortable drivers seat and a clunk I hear sometimes when accelerating from a stop or a slow roll.
The passenger seat is very comfortable, but someone did something to the drivers seat. It feels maybe like the foam rolled down and is now pushing against my lower back. I was so busy listening for noises and so forth on the test drive that I forgot to check for comfort. But everything seems to work on this car. I plan on babying it until the day I can afford something more exciting to drive.

Only complaints I have are the boring styling and the miserable turning radius. Besides the seat and clunking sound, this is a great car. What problem areas should I be looking for?

Congrats on your purchase. I had a 2002 Maxima, which led me to the i35. I liked it so much that I bought another, and another. They are all long gone, but the memories still linger.
I too despised the turning radius, but loved the way that VQ35 pulled at 4,000 rpm. The i35 front was more beautiful to me, with the smokey headlights.
The platform was fairly customizable and you could buy suspension components to ride as stiff as a go-kart or smooth as butter.


Anyway, on to your questions:
Comfort
I felt that the general ergonomics of these vehicles were among the best I'd ever encountered. The i35 especially had very comfortable seats.
Heated front & rear seats + steering wheel was a nice touch for the year, when equipped.
Decent BOSE radio, for what it is

Clunking noise
Probably the left (front of the vehicle) motor mount. That is the fluid filled one, and the rubber deteriorates, spilling the contents. Easy to check as you can put it in park and aggressively snap on the throttle pedal. You'll hear or see the engine jump & drop.
If the clunking were non-takeoff related, like over speed bumps & such, then we'd be looking at the suspension.

What to look out for
1. Rattling timing chain. Basically, plastic timing chain guides were originally used, which would cause excessive chain slap when they broke & slipped. This happened at various mileages. Newer designs fixed the flaw by a harder material I believe.

2. Oil consumption. Could be as bad as 1 quart every 1000 miles, depending on your driving habits or the particular engine's inherent state.
As a bonus, when your chain starts rattling, it's an indication/ reminder that oil is low.

3. Rear wheel well rust. Not sure where you are located, but this is a major phenomenon in salty winter areas. If a concern, I'd just check it and perhaps seal it.

Thank you so much for the reply.

OMG, Infiniti still used the plastic timing chain guides, even after the early Q45 debacles!? I had a 1990 Q45, and not only did it have transmission woes, but it had plastic timing chain guides that broke not if, but when, which supposedly caused engine detonation. Is it possible to tell if my year of car had the harder material? If the guides break, will engine failure (and need for rebuild) happen. Does the chain need to be replaced. The only time I hear a very brief rattle sound is at a cold start up.

The Bose subwoofer isn't working. No vibration or sound from it. Is this an expensive fix/replace?

This is a Texas car, so I haven't seen any rust. Any idea of the cost to replace and engine mount? I'm pretty sure that's what the problem is, and not suspension.

Again, thanks for the reply.

Fixed the seat problem...well, found out what caused it. Didn't know it had lumbar support :-) Now it's comfortable.