Couple of times in the morning I noticed that the skylight is foggy in the center (see picture below). No other windows are foggy. The temperature/humidity is outside 50F/77% inside, 70F/44%. Does this indicate a problem with the skylight?
It's possible that your double pane glass has failed. You should examine it closely under less extreme conditions. If the interior has a "fog" in normal conditions, then the gas has likely leaked out. Sealed window assemblies are only warranted for about 10 years. Some last longer than that. YMMV
I replaced all my Velux window panes a few years ago, when I was getting the roof redone. They were fogged and had interior condensation frequently in the winter. I contacted the manufacturer, and was able to special order replacements via the local Home Depot. Though it can depend on if the model is still in production.
If cold, moist air is comming in from outside, then it would be unlikely to condense on a warmer (interior) surface. Condensation occurs where there is high humidity in a warm environment, which becomes cool. In this case the temperature inside is higher.
44% humidity doesn't sound very high, but at 70 °F it has about 0.26 grams of water/vapor per cubic foot. At 50 °F (the temperature of the skylight-glass) the humidity (of 0.26 grams of vapor per cubic foot) would be about 92%. So, general condensation is a viable explanation- especially if the cool surface is just-right for condensation. But I would still take a closer look.
The test that I would perform, to see if the skylight was airtight, would be to light some incense under the window and then go onto the roof to see if any smoke is escaping. If not then, then after all the smoke has cleared, I would try again, but this time I would put a box over the skylight and put the incense under the box. Then go back inside to determine whether air is comming in through the skylight. If you cannot find evidence of a leak, then your best options are to treat the surface of the skylight with an antifogging solution or film, or use a fan to help circulate air (usually it helps), or you could opt for a dehumidifier.
There are many DIY antifogging solutions (see thread: Is there a technique to make a shower mirror fog-free?). But some of the listed solutions actually cause more condensation, allowing a water film to occur, which is easier to see through than condensation.
Probably the skylight's fine - this is similar to the condensation on car windows when you drive out of a cold garage on a warm humid day. The reason vertical windows are less foggy could be some combination of (1) the windows are double-pane insulated, (2) the airflow along the exterior walls differs from the flow along the roof.
You didn't indicate whether these are fixed or openable skylights. If the latter, check to be sure the drive is fully closed.
BTW, if there's an exterior leak, you're far more likely to see water dripping along the box edges when it rains.