Teleconverters or as Canon calls them Tele-Extenders (TE) are added to a lens to increase the focal length by inserting negative elements between the lens and camera. They have been in use for decades and are rather simple optical devices. In the case of the Canon 1.4 II there are 5 glass elements and no moving parts. I have never heard of anyone having a defective one at least in terms of optical performance. It is commonly believed that only a very good prime lens would tolerate a TC, most of the older zoom lens would not give acceptable results with a TC. 
 

Whether to use a TC to increase image size or to "'rez up" the image in your photo editor was always a subject of debate. Back in film days (prior to 2003) I had performed a test with my Canon 300 f4L and Canon x1.4 Tele-Extender to determine if there was any benefit in using the TE. Several Fuji Pro via slides were shot and scanned into the computer and compared under magnification. At the time I determined there was an advantage in terms of visible detail in the image to using the Tele-Extender vs rezing up the image without the TE. 

Tele-Extenders increase magnification but reduce resolution by a certain amount. The image size gain of 140% is partially offset by the resolution loss usually around 15% for a 1.4 TE according to my tests but also a loss of contrast which is clearly visible but harder to quantify.  Indeed Canons own modulation transfer data (the modern measure of lens performance) shows a significant loss with TEs on all the "L" lens. Tele-Extenders cause the lens system to exhibit chromatic aberration, this can be seen as purple\green color fringing in high contrast areas of the image and it gets progressively worse towards the edges\corner of the frame. All of Canons long telephoto lens are well corrected for chromatic aberration by themselves but adding a Tele-Extender clearly causes purple\green color fringing. 
 

When I acquired my first digital camera in 2003 I again  tested with and w\o a TE and I recall I still found a benefit to using the TE over rezing up. Lately however I had noticed in the field that my images using my 500mm f4L IS  without the TC seemed to have the same amount of detail as the TE ones.  Newer digital cameras have more resolution than the  6 megapixel 10D  and I have been using a Canon 50D of late with it's 15 megapixel sensor. The detail in an image is limited by both the lens sharpness\contrast and sensor resolution. In the 10D era the sensor had less resolution than the lens could provide but with the 50D the sensor resolution and the lens resolution are similar. With the 10D, loosing some resolution by adding the TE did not reduce the image detail significantly but with the 50D's higher sensor pixel count I began to suspect that the lens\TE combination was now limiting the detail more than it had in the past.
 

With this idea in mind I decided to test image detail for the straight 500mm and 300mm at optimum apertures vs x1.4 and x2 at optimum aperture. The test was performed indoors by shooting a target at a distance of 10 (300mm lens) and 15 feet (500mm lens) using a tripod and flash, necessary to insure camera shake does not impact results. Even slight focus errors can throw the test results way off so I mounted my lens on the Arca ball clamp, focused on the target with autofocus, one shot mode, then switched to manual focus placed tape on the lens focus ring so it would not move and then shot several images of the test target with different focus distances by sliding the lens foot through the clamp 2 mm at a time about the point of focus. The idea was to  select the sharpest (best focused) image by looking at them under high magnification on the computer screen and selecting the best (sharpest image). 
 

All images were shot in RAW and converted to TIF with no sharpening used. The best focused images were selected and comparisons were made between the different apertures. The best aperture for the straight 500mm was f5.6, for the 500mm x1.4 it was f8 in line with what I know from use in the field. The 300mm is best at f4 or f5.6 by itself and f5.6 with the x1.4 and f8 with the x2.
 

I then compared the images side by side on the computer screen with the non TE image rezed up 140% to match the 500 mm x1.4 image. The 300mm was compared with x1.4 and x2 TEs. Part of the target near the center and the corner was compared at a screen magnification of 300% where pixels are just becoming  visible. 

The above test procedure was performed with the 10D and the 50D. The image target used was a Canadian 10$ bill with a grid pattern for the focus point target. Crops from near the center and left corner approximately 60% off center were used for the comparisons.

To be sure my x1.4 TC was not defective I repeated the same tests with a borrowed Tele-Extender (thanks Lat) and tested again but did not see any difference.
 
 

Results and comparison images:

50 D image 500mm f4L IS
Centers were slightly better with the x1.4 TE image compared to rezing up.
Corners were moderately worse  with the x1.4 TE image compared to rezing up.
Centers were slightly better with the x2     TE image compared to rezing up.
Edges were slightly better with the x2     TE image compared to rezing up.

50 D image 300mm f2.8L IS 
Centers were significantly better with the x2 TE image compared to rezing up.
Corners were moderately  better with the x2 TE image compared to rezing up.
 

10 D image 500mm f4L IS
Centers were moderately  better with the  x1.4 TE image compared to rezing up.
Corners were slightly better  with the  x1.4 TE image compared to rezing up.
 
 
 

Disadvantages of using a  TE:
1 - slower autofocus performance, often significantly. Canon Prosumer bodies will not autofocus with X2 TEs on the 500mm f4 as they need f5.6 or faster
2 - requires stopping down for best sharpness effectively loosing 2 stops for a x1.4 TE
3 - dimmer viewfinder image do to the light loss of 1-2 stops
4 - chromatic aberration (color fringing) particularly off the center of the image and more noticeable in high contrast areas
5 - adds weight, a problem when doing flight shooting and traveling
6 - allows dirt to enter the camera while changing
7 - lens mount pin contact related camera errors are more frequent

Advantages of using a  TE:
1 - slight gain in image detail over simply rezing up
2 - viewfinder image is larger in the frame and may aid composition
3 - reduced angle of view may reduce background clutter in some situations.
 
 
 

Conclusions:

1 - TEs give best results towards the center of the frame, color fringing gets progressively worse off center
2 - With the 300mm f2.8 TEs produce significantly more detail at frame center and a moderate gain near the edges .
3 - With the 500mm TEs produce slightly  more detail at frame center and  little or no gain near the edges.
4 - The 1-2 stop loss of shutter speed may often offset all resolution gains in the field!
 
 

Notes:
1 - Lens used was my 500mm f4 L IS add 300 f2.8 L IS , Teleconverters were  Canon EF 1.4 MKII and Canon  EF 2 MkII 
2 - The 50D Autofocus  was bang on do to having previously set up  the AF micro adjustment, the 10D was off but only about 2 mm.
3 - Modulation transfer function explained
4 - Rezing up was done with Corel paint Shop Pro  ver 10.03,  "Smart Resize" function
5 - Tests were done at ISOs of 125 and 200 to produce low noise images
6 - Ef Lens Work III