Queen's Parade, Clifton Hill

Location: Queen's Parade Clifton Hill, between Delbridge and Grant Streets. 
Council: City of Yarra, although this may also involve VicRoads or Dept.Transport. Unsure.
Responsibility: There are a large number of possibilities. Try starting with MD
The Problem: There you are, slogging north-east uphill to escape the city fumes, on a nice wide Queen's Parade cycle lane, up to the the Clifton Hill shops. OK half of the lane becomes unrideable bluestone. Suddenly, the cycle lane disappears. No signage, no explanation. Traffic roars behind you, now with impunity. You can carry straight on, ignoring the bluestong gutter that tales up most of the lane and launching onto the unmarked tarmac ahead - unmarked except for the remnants of the old dashed cycle lane that was once there,  that is. Most cyclists do this.
The others veer left onto the safer access lane, pictured. There, you trundle on, veer right again, until the lane starts up again, 60m further on.You need to do that to get to the traffic lights.
This an extraordinarily crap solution to road sharing.
Solution: All that bluestone gutting and grass could house a lane you could actually ride on. But that would cost more money. So let's just leave it to cyclist's intuition, shall we? How about some signage at least?
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Swanston Street/Faraday Street, Carlton

Location: Corner of Faraday St and Swanston St, Carlton.
Responsibility:

Council: Melbourne City Council

Description: Approaching the busy Swanston Street near the University of Melbourne from the east, travelling down Faraday Street, you encounter this strange bit of green cycle lane just a few metres long. Nobody I know has any idea what you are supposed to do when you reach the end of it, and it seems to serve no purpose (I noticed the photo shows a sign, in the second photo-it has taken me 3 yrs to notice that!). There is a cycle lane on the road, which was painted in a bit later. Had you wanted to turn left, there is a clear marking on the road to do just that. Should you want to progress across Swanston Street to the University, on what is rather unfortunately called "Monash Road", there is a nice wide track to do that, after a large gap and a crossing. You might as well stay on the road to do that, too. So maybe there is a hyperdimensional portal at the end of the green lane. That would explain why you never see anybody using this crap cycle lane.They just disappear.
Solution: Why not just leave it there as a monument to Melburnian infrastructural puzzlement?

Gardiners Creek Trail between Glenferrie Rd and the Yarra Trail

(incomplete - not ridden it)
Location: Gardiner's Creek Trail, Boroondara and Stonnington Council
Responsibility: VIC Roads and local councils
Problem: See here for the problem. http://boroondarabug.org/wiki/Gardiners_Creek_Trail_-_two_problems. In addition, this site has substantial information and sugegstions for further improvements along the longer trail length. The conclusion is that Boroondara council has done a far better job of making a sensible and useable trail than Stonnington.
Solution: see above site. "If only we could Boroondara-ise the whole trail…"

Gipps Street, Abbotsford

Location: Gipps Street, Abbotsford

Responsibility: Yarra City Council

The Problem: Volumes have been written about the "Gipps Street Steps" on the Capital City Trail along the Yarra. Following the River path southward, it ends in steps before crossing the river east-west  at Gipps Street.  They are three flights of steps up that mar a pleasant commuter and leisure route (Bicycle Victoria image). They leave you winded and annoyed (on a bike or with a pram) or stranded (if you can't make it up or down).

The Solution: In 2009 it was reported that there is finally some action on a new bridge design, pushed by Bicycle Victoria. Then on 5 May 2010, BV reported that the state budget had allowed $2.5m for a complete redesign and solution, funded through the Parks Asset and Replacement Program (Parks Victoria).
The details are here. Nice one. 
For the next few months, or maybe over a year, keep slogging...