The weather forecast often says frost or patchy frost while predicting lows well above freezing. Also, it often gets below freezing while the dew point remains low enough to avoid frost. Which of these conditions do I need to worry about for protecting citrus?

I just brought my trees back outside for spring and NOAA is predicting 38F & patchy frost.

Depends on the variety of citrus and the conditions. If the tree is in bloom you want to protect it. If not, most varieties of citrus can take a light frost without a problem. Madarins and oranges can take a heavy frost without much problems.

Patchy frost means isolated places.

Normally frosts occur when air temperature are around the freezing point of water. But frosts can form even if air temperature is 40 deg F. And frost may not form when air temperature is at 30 deg F.

What you should worry about are the clear moonless night skies with calm winds which are perfect for frost formation even if the air temperature are within 8 Farenehit degrees above freezing. If you are in a low lying area where cold air drains into, then you could have greater chances of frost. If air temperature is above freezing, a simple drape of jute sack or old bed sheet over the top canopy provides adequate protection. Misting with water over the canopy will work. A small fan directed on top of the canopy will also work if you want to conserve water.

A few have blooms so I will bring those and the key lime in, thank you.

Key lime is the most sensitive of all citrus to my knowledge and should be protected from exposure to any temperatures below 40.