Before I comment I have to ask your training habit: Do you fly one lesson each week, or only occasional lessons because you're so busy, or 3 flying days each week, or full time?
Sometimes life gets in the way
In terms of progress, 70 hours and just starting cross country flights seems to be on the slow side. But then, if you're not training regularly, you can't blame the CFI for spending some time reviewing previous materials during each lesson.
Ideally, the flight lesson pre-flight should go like this:
CFI: Today we will be practicing steep turns. We will takeoff, head North to this area on the chart and practice there. Then we will fly North East and proceed to this airfield to practice some touch and go. Our weather report says there is weather system South of us, we need to keep an eye on it in case it moves North. I will work on the radios and navigate, you will be doing all the flying. Questions?
This establishes clear goals of the lesson. A good lesson should also conclude with a post-flight debriefing:
CFI: Today I noticed that you did not enter the traffic pattern correctly. You entered like this, which is not good because of that, that, and that. Given the situation, you should have went like this. We will be practicing more traffic patterns in our next lesson.
If the agenda is driven by the instructor instead, you'll get more benefits:
- The goals of the lessons are clear.
- The instructor can adjust lessons based on your weakness. For example, if you were rather sluggish during engine-out emergencies, the CFI should review emergency procedures with you on the ground and give you more practice in the air.
- You may not be aware that you are not getting enough practice in some areas.
- You can prepare for the next lesson ahead. For example, if your next lesson is a cross country, you can review flight planning, navigation principles & airspace regulations.
Is your situation normal? I'm not an instructor so I don't know, but it can be better. Then again, if your flying schedule is rather random, learning efficiency would be lower, and you end up spending more flying time and money.
Now, falling asleep......To me, this is a big No No. I am just a student. I have not been certified (yet) that I can operate an airplane safely:
- What if I make a navigation error and end up heading to Area 51?
- What if I'm heading into IMC and need to turn around?
- What if the fuel level is reducing at a dangerous rate but I didn't notice?
- What if I got a stuck elevator?
A flight instructor is seated in the same cockpit with the student to correct mistakes or react to situations in a timely manner. To fall asleep during a flight lesson is an irresponsible behavior to the student and other people on the ground who might get hurt if your plane crashes.
Of course, flight instructors are all humans and we all tend to make mistakes. Perhaps he was overstretching himself. Perhaps he got a family emergency the night before and stayed up really late. If it was just one flight, I would pass but keep an eye on. If it happens continuously, it might be a good time to turn away and look somewhere else while you're still safe.