Is the melting pattern on this roof a sign of really poor insulation in the knee walls? Thinking about purchasing, but I don't want to spend my life fighting a poorly designed/insulated house if it's a hard fix.
It is very difficult to tell based on a photo. There are a number of factors that could indicate insulation problems and melting patterns is one of them. But it depends on the current outside temperature, sun exposure, how well the shingles absorb heat, wind conditions and how hot the interior is.
I'd say a better way to determine if there are issues is to examine at the utility bills. The seller should be able to provide them. Realistically the insulation is there mostly to keep cost of heating down so the expense should be a decent indicator of how well insulated the house is.
Another thing that will indicate poor insulation is if the room feels cold. Let's say the temperature on a thermometer in the room reads 72°F but it is not comfortable. That's another indication that the walls are poorly insulated. It happens because the heat radiated from your body is not adequately radiated back from the wall. You can also place the back of your hand on the exterior wall and quickly compare it to an interior wall. Knee wall cavities are often problematic due to confined work spaces upon construction and limited soffit ventilation.
If all the houses around have snow on the roof this one is the only one that doesn't, it's probably not well insulated.
A good guess would be warm air infiltration from the floor below, plus not enough insulation. It is very hard to install enough insulation, using today's standard insulation rules in that type house design. Since there is no attic or even a crawl space above that living area, there is not enough space in the roof joists to get a proper amount of insulation and recommended venting space. As an example, if the roof joists are 2X6's that 5 1/2" free space only allows for R-19 batt insulation with no vent area above the insulation. my 2 cents.