Was there really a caste system in vedic period as it is perceived today by many?
Yes, there was a birth based caste system in the Vedic period. This section of the Yajur Veda talks about it:
From the breast and arms he meted out the Pañcadaça Stoma. After it the god Indra was created, the Tristubh metre, the Brhat Saman, of men the Rajanya, of cattle the sheep. There fore they are strong, for they were created from strength.
With little to no knowledge of our scriptures now, can a person born in a brahmin family can rightfully be called a brahmin just by the virtue of his birth in that family?
Caste is based on birth. Based on karmas done in previous lives, one is born in a particular caste. A Brahmana who doesn't know the scriptures is a bad Brahmana who has failed his Varnashrama Dharma, but he is still a Brahmana.
The idea that caste is determined by quality is entirely fallacious and impractical. Take for example, a person who is religious and very strong. If we go by the theory that caste is solely determined by qualities, then what caste would you assign this person? One can say that since he is religous, he is a Brahmana who happens to be very strong like a Kshatriya. But at the same time, one can say that since he is very strong, he is a Kshatriya who happens to be religious like a Brahmana. So since most people have qualities that belong to every caste, it is not possible to determine their caste through qualities.