How can you tell if a 3 year-old child has a learning problem?

Hard to predict. While some would suggest a kid may have ld issues if they are speech / language delayed at 3, many areas of learning are not "testable" ntil the kid is older. Just like you can't know if a 3 day old will walk at a normal time, u can't get at spelling, coding, short or long term memory, math or other areas until the kid is old enough to test in those areas.