How do I know if condiments in refrigarator are good?
A really accurate answer would require analyzing each individual condiment, but there are some general principals you can apply.

Some condiments would be shelf stable outside of the refrigerator because they inhibit pathogen growth by being:


acidic, like ketchup or vinegar
salty, like soy sauce or Worcestershire sauce
sweet, like jam or jelly, or chocolate syrup
sufficiently dry, like peanut butter


These are not going to be bothered by a day or two outside of refrigeration.   We keep them in the fridge because it extends their shelf life to be much, much longer, on the order of months instead of weeks.

Of course, you should still discard them if you see any signs of mold, unusual wateriness, or strange smells.

Other condiments in the refrigerator such as mayonnaise and salad dressings should be considered subject to the normal rule for how long foods can be outside the refrigerator.   This would normally be a cumulative period of about 2 hours maximum, to be on the safe side.

While normally I would not mention any... more liberal... interpretation of the best recommended safety standards, I will point out that 60 F, while technically in the danger zone, is still moderately cool, and the danger increases exponentially with temperature.   You can assess your own risk, but you may decide a few more hours is still a risk you are willing to accept.

As always, check for off smells, colors, or appearance of mold or other spoilage, and apply common sense.

See also:  How do I know if food left at room temperature is still safe to eat?