In so far as there is any cycling infrastructure in Oxford it is substandard, but some of it is so bad it is actually dangerous and should be removed. (In some cases its presence also obscures the need for proper infrastructure and better road design.)
Here are a few examples, with suggested solutions (starting with the better ones and moving towards easier but less effective ones). If you have any suggestions for additions to this page, add them in the comments, or email me and I will add them to this page.
The door-lane cycle lanes on Warneford Lane
As well as being in the door zone, these lanes are impossibly narrow. Given the narrowness of the parking spaces, even reasonably well parked large vehicles can protrude 20-30cm into them, giving them an effective width close to zero, if not actually negative. The marked "lane" is about 1m wide, but IAN 195/196, Cycling and the Strategic Road Network gives the recommended width for a cycle lane here as 2m (assuming peak hour cycle flow is less than 150/hour), with a 1.5m absolute minimum, and requires an extra 0.5m if there is a vertical obstruction higher than 60cm adjoining the lane. This is also a very busy section of road — I would guess around 4000 motor vehicles a day, including some buses — so cycling along it in peak hour can involve half a dozen close passes.
Cycling in the main carriageway is much safer here but, because of the huge median separation, drivers tend to speed (as Graham comments below, the speed limit is 20mph, but 30mph is common) and some get angry at being slowed to even 15mph. The marked cycle lanes encourage them to "push" cyclists to the side.
Solution 1: Remove the car parking, put in physically separated cycle paths. (Would need reworking of the roundabout and junction at either end to make those really useful, but it would be a start on making cycling here possible for anyone who can ride a bicycle.)
Solution 2: Remove the "cycle lane" markings, put bicycle symbols in the middle of the carriageway and signpost the whole section "narrow road, do not overtake bicycles". Drop the speed limit to 15mph.
Solution 3: Remove the painted cycle lanes and do nothing else.
The northbound cycle lanes on Longwall St
Going north on Longwall St, the cycle lanes are both too narrow and appear and disappear abruptly. They push cyclists away from the centre of the lane and thus encourage motorists to overtake just as the road approaches a blind corner, which is dangerous for everyone concerned.
Solution 1: Block Longwall St to all motor traffic (except emergency vehicles). At its narrowest, it's just wide enough to fit proper cycle paths and proper footpaths.
Solution 2: Make Longwall St one-way for motor-traffic. A protected contra-flow bicycle path could then fit in the narrowest section, along with adequate footpaths and a shared motor-vehicle-bicycle lane (marked "do not overtake bicycles").
Solution 3: Mark the entire narrow section of Longwall "Do not overtake bicycles" and put bicycle symbols all over the carriageway. Drop the speed limit to 15mph.
Solution 4: Remove the northbound section of painted cycle lane and do nothing else.
Note: I've added an extra "Solution" to both my examples, that being to remove the painted cycle lanes and do nothing else. Which is really my criterion for "so bad it should simply be removed".