Does the Doctrine of No Soul mean there is nothing permanent to continue? Does the doctrine of no soul is means that there is nothing permanent to continue? So is the teaching of reincarnation, rebirth misleading as there is a notion there is a continuity after death? Also death and birth is visible at the physical level, [but the rebirth process is not. What is the implication on this in the doctrine?]
I agree with you.

The Pali suttas do not refer to a continuous consciousness at the termination of life. 

Instead, the suttas explain 'birth' ('jati') &amp; 'death' ('marana') refer to the birth &amp; death of 'self-views'.

Therefore, 're-birth' refers to the re-arisings of 'self-view'. 

For example, you make $100,000. Re-birth is the happy view: "I made $100,000; I am rich". You lose $100. Death is the unhappiness of 'I lost $100; I am poor".