Your 3 year old is NORMAL, per this age-set and development.
Kids this age, and even in Preschool, Kindergarten, WILL GET THE SEQUENCING mixed up. It is normal.
"Sequencing" and this type of "logic" is a whole different thing, versus just "memory" or other things or trivia.
PER my Daughter's Preschool Teacher, when my daughter was at that same age, and when she was 4 years old... MANY MANY MANY kids are STILL just learning these things. Its okay. They don't have to have it down pat, yet. AND, when they start writing, they WILL get their writing mixed up too... at this age, it is to be expected. Even 1st Graders get their writing mixed up. Their brains are developing as well still.
One other thing... the best way to 'teach' kids at this age through 8 years old is through auditory approaches. ie: making SONGS and rhymes about things. My Daughter's Preschool Teacher said this, and at 3 years old, the kids were learning Broadway Plays/songs, the 50 States, the Presidents of the USA, the days of the week, the 12 Months, the seasons, the planets, and many other things. They learned it all through AUDITORY based approaches. Nothing hard-core and repetitious... but just learning it by way of songs and simple dance movements. It is amazing. They didn't sit at desks or have anything written down, but it was all through play-based activities. They only spent about 10 minutes a day on each "song"/subject. NOTHING rigorous. Just all in fun. To this day, my Daughter who is now 6 years old, STILL remembers what she was taught in Preschool at 3-4 years old.
At this age, you don't want to spend more than 10-15 minutes on a "subject." Even 15 minutes is a long time for a 3 year old. Mostly, just have fun... and intersperse your daily talking with "lessons"... for instance, "Mommy is cutting an apple. "A" for apple..." or, sing songs about it. For alphabets/numbers, concentrate on no more than say 3 letters at a time. Then over time, build up.
I know that nowadays, kids are expected to be so accelerated... but not that it is the best thing developmentally.
Your son is going through a sleep phase or is changing developmentally, or separation anxiety. MANY kids go through this. Is should pass. Has he "night terrors" yet?
Here is a good link:
http://www.babycenter.com/0_how-much-sleep-does-your-chil...