The quality is what I would expect to get running remotely. There are a few things that I I noticed with your captures.

1. Your connection speed varies from 278k-1222K. With these speeds, you'll only get the 320x240 resolution. What is your upload speed at your location?

2. Your first two screen captures are in the 4:3 format. That means those channels are not HD.

3. What kind of service do you have connected to your Tivo Series 3? And how are you connecting to the Slingbox? The HD Connect? If so, why is your signal 4:3 in some windows and 16:9 in others?

1500 Sounds like a possible number for your upload speed. Do a speed test to get an accurate reading.
http://www.dslreports.com/stest

I would say that 1500 is maybe, barely, just might be enough to get 640x480 resolution. Which would be the max resolution you can get out of a Slingbox Pro. If you do have that speed. Try setting the resolution manually to 640x480 in the Slingplayer software. If it stutters constantly, you don't have enough bandwidth to do it.

Now, what doesn't make sense to me is your statement that you manually changed the Slingplayer format to be either 4:3 or 16:9 depending on what you were watching. The reason I question this is because, the Slingplayer streams what you're feeding it. And if you are connected to an HD television, then the stream going from your Tivo to the Television would only be 16:9 And you would get grey/black bars on the sides of any signal that was 4:3 or a stretched picture. And as evident in your captures. You have neither. That just doesn't make sense.

All you can do is crank the settings up. Keep going till it starts stuttering then back off 10-20% to allow for other internet traffic at your slingbox location. Sounds like you've got it under control now.

1. The Aspect ratio on the slingplayer doesn't change itself.

And for that matter, it shouldn't change on your Tivo either. Usually, people have a single output from the tivo. If you have an HDTV then that output is 16:9. So, the Tivo presents you all the signals from the cable provider to the TV as 16:9 in some fashion.
HD Channels are already 16:9
SD Channels are 4:3 so they are either stretched to fill the screen, scaled to fill the screen or left in their normal aspect ratio and have black/grey bars on the sides to compensate.
Do you see any of these?

2. BitRate - The higher you can go the better. This is the amount of compression in terms of the video data coming across.

i-Frame - Every once in a while, the slingbox will send a full frame across the network, This prevents images from smearing. The way temporal compression works is this... The Slingplayer analyzes the whole screen and sends you what it thinks you need only, to save on bandwidth. So, for instance, A news reporter scene would send only his head if he is talking and the rest of the image is static. While a Sports show would need to send you everything all the time because the camera is moving. Since it is dependent on the shows you are watching, You're going to have to experiment with this setting.

Audio Bitrate - Now.. This is where you can save a bit. This is the amount of compression in terms of the Audio. Imagine listening to a 60k MP3 vs. a 320K MP3. The higher the number the better the sound quality, but you may not care about the sound as long as it is good enough.