How long should the first step of dissolving the jam sugar in the vinegar over a low heat typically take? I made one batch and confess to loosing patience and so 'gave it a poke'. I now know why you should not stir it - because it creates a 'scum' which I picked out before bottling and the results are clear. Unfortunately having to eliminate the cloudy bits meant I hadn't made sufficient jars! I made another batch this evening and left it until the sugar was all dissolved which took about an hour. Followed the remaining steps, boiling for 10mins but the jam seemed more like toffee!
When you are making jams, jellies and caramel it is important not to stir the sugar mixture, particularly when it is boiling. Stirring will cause the sugar to crystallize and leave a cloudy mixture. The "scum" mentioned is probably crystallized sugar. It is normal to get a small amount of foam on top of jam or jellies after boiling, but this can be skimmed away with a spoon before jarring the mixture and should not be a large quantity.
When you first put the sugar and vinegar in the pan then you can give the mixture a gentle stir. This will help to start dissolving the sugar and stops it forming a clump at the bottom of the pan. Once the pan is on a low heat then it can usually take anywhere between 10 and 20 minutes to dissolve the sugar. It will depend on the size of the pan and the heat under the pan. You should also make sure that there are no crystals of sugar left in the mixture before it is boiled.
If the mixture is like toffee then it is most likely that the mixture had boiled for slightly too long. The setting point is reached when the mixture reaches 105c/220F and that will be when enough water has been evaporated from the mixture. If you spent a long time dissolving the sugar or a re using a large pan then the setting point can be reached with less boiling time. If you are not sure of the setting point then it is helpful to use a jam or candy thermometer, or use the "cold plate" test for a set.