All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
Indeed, minor sins are quite serious in Islam, and the Muslim is enjoined to avoid all sins, be they minor or major. In fact, committing minor sins leads to committing major ones; when the person becomes rather lax and takes committing minor sins lightly, thinking that they are less grave and serious compared to major sins, then such laxness may lead him to adopting an indifferent attitude towards committing sins, thus leading him to commit major sins as well. Also, a person may mistakenly assume that a major sin is a minor one out of ignorance and lack of knowledge; Allaah, The Exalted, says (what means): {...and thought it was insignificant while it was, in the sight of Allaah, tremendous.} [Quran 24:15] The Prophet said, "Beware of minor sins, for they accumulate until they doom a man,” and the Messenger of Allaah gave a likeness of that: “Like people who camped in the wilderness, and one man brought a stick, another man brought a stick, and so on, until they accumulated a lot, then they lit a fire and cooked their food." [Ahmad and others]
Therefore, a Muslim is enjoined to avoid all sins and repent of whatever sins he has committed, major and minor alike. He should not take it lightly, otherwise he may incur his own destruction while being unaware of it. For more benefit, please refer to fataawa 116246, 88207and 196779.
Ath-Thahabi listed seventy major sins, as you have mentioned, and other scholars listed more than seventy; Ibn Hajar Al-Makki listed four hundred and sixty-something major sins. Some of the major sins that he listed are questionable though. In any case, the scholars from the righteous predecessors differed about the exact number of major sins, as is well-known. The clearest view in this regard is that the major sin is the sin about which warnings have been reported, either of a curse, or incurring the wrath of Allaah, or earning Hellfire, or becoming liable to a hadd (i.e. the corporal punishment determined by Islamic Law) in the worldly life.
Allaah knows best.