I'd like to discuss the following points:

1. limited amount of positions for each function.
2. getting a job.
3. available careers.
4. career rewards.
5. customisation.

1. limited amount of positions for each function.
There can only be one mayor for example, but elections could be held to give other political sims the chance to become mayor.

Generally the further a career advances, the fewer positions there should be available. Should be exeptions of course since a newspaper office would not require that many delivery boys/girls but would require more writers.

Through this system jobs will become more meaningfull, and sims will have competition for some promotions. Maybe it could even allow sims in the right position for it to be able to promote other sims who work further down the chain of command.

2. getting a job.
While it shouldnt be that hard to get a job since it can be frustrating enough in real life, sims could have a short job interview before getting hired. A good mood would generally help a sim getting hired, but traits could also have a positive or negative effect based on what they apply for. Insanity might not help when you want to become a cop.

Additionally, your sim could be put in a higher position right away if they have good skills if the job allows it.
Being very athletic shouldnt mean your army sim doesnt need to go through basic training, but in the office you could get a higher position.

3. available careers.
It seems there are always 10 careers to start with, and I'd like them to upp that a bit.
Here's the branches I suggest the game to start with:

-Medical.
-Law Enforcement.
-Construction.
-Office. (multible offices with different products.)
-Millitairy.
-Political.
-Laboratory.
-Music.
-Sports. (various sports as seperate careers.)
-Criminal syndicate.
-Education.

Aside from this, all the NPC jobs should be available as well as minor careers with just a few tiers in it or none at all.
Maid, fireman, store clerk, hair dresser, gardener, etc. it could all be available to your sims.

Regarding sub branches, I'd like to see more of this.
Music career could allow you to choose a position based on any instruments in the game. Possibly divided based on symphonic and rock branch and some for both.

4. career rewards.
It's nice to have benefits with a career, but they should make sense.
A sim working in construction could eventually get a discount on everything thats done at his house in build mode. He'd have friends and his own skills to do it cheaper after all.
A drill, a workers van and various other job related items could be unlocked along the way.

Lab workers could get a special alchemy set that allows for a few additional bottles to be created that cant be created otherwise. these things could possibly be more dangerous ones.

5. Career customisation.
I'd like to be able to set some specifics for any career, options differing for each career.

Millitairy base could be set to be airforce, marine or infantry.
This would result in different advancement.
For an office, it could be selected what kind of office it is. they could make commercials, publish a magazine, a newspaper, or maybe its for game design. It could also be named.

Furthermore, the career outfits should be customiseable for each rank. It could also give the option to select formal wear, casual wear or athletic wear for it so the sim will wear their own appropriate clothes instead.
Available options for career outfits could be based on the career.

I agree with all of this but I would also add that the option to decline a promotion should be available. If a sim joins a career line and manages to turn up to work each day for a few weeks, it shouldn't automatically mean that they end up running the joint.