First of all, it is not an advantage to have a Bible that "never changes". There are continually new manuscript finds that improve our understanding of the underlying text, just as there have been philological advances that result in an improved understanding of obscure and difficult terms in the text. That is why many translations go through subsequent editions.
Second, it is not true that the NWT never changes; there have been minor alterations between the initial (1950 for the NT) edition and the 1971 and 1984 revisions. Some of these correspond to doctrinal and social changes in the Society, but not all.
1950 edition: "Again Jesus cried out with a loud voice, and ceased to breathe".
1971, 1984 editions: "Again Jesus cried out with a loud voice, and yielded up [his] spirit".
The 1984 edition places "ceased to breathe" in the footnotes. This is a very minor change, but possibly the original wording was motivated by a reluctance to view a person's spirit as something that can be yielded up. But since some other translations render the expression similarly, this is not necessarily the case. But it is noticeable here because the NWT aims to be a literal translation and the non-literal "ceased to breathe" is a departure from this pattern.
1950 edition: "Originally the Word was, and the Word was with God, and the Word was a god. This one was originally with God".
1971, 1984 editions: "In [the] beginning the Word was, and the Word was with God, and the Word was a god. This one was in [the] beginning with God".
The less literal rendering in the 1950 edition is verbally more awkward and it could be (mis)-read as implying that the Word's existance precedes that of God, or was of equal eternity. The later rendering is more literal but also could be interpreted more easily as implying that the Word's existence had a beginning with the creation of the universe.
1950 edition: " And he gave some as apostles, some as prophets, some as missionaries, some as shepherds and teachers, with a view to the training of the holy ones for ministerial work" (Ephesians 4:11-12).
1971, 1984 editions: "And he gave some as apostles, some as prophets, some as evangelizers, some as shepherds and teachers, with a view to the readjustment of the holy ones, for ministerial work, for the building up of the body of the Christ" (Ephesians 4:11-12).
The emphasis in the Knorr years was on the international expansion of JWs and Gilead as a school for training missionaries. But during the Vietnam war and in following years, the emphasis turned to defining all baptized JWs as "ordained ministers" (cf. 1 February 1967 Watchtower, pp. 366-372; 15 June 1967 Watchtower, pp. 521-523; 8 January 1971 Awake!, pp. 13-15; 15 March 1981 Watchtower, pp. 14-17, etc.).
1942 KJV published by the WTB&TS: "And ye, fathers, provoke not your children to wrath, but bring them up in the nurture and admonition of the Lord".
1950 edition of NWT: "And you, fathers, do not be irritating your children, but go on bringing them up in the discipline and authoritative advice of Jehovah".
1971, 1984 editions: "And you, fathers, do not be irritating your children, but go on bringing them up in the discipline and mental-regulating of Jehovah."
This gradual shift to a stricter stance is thought to reflect a tightening of Watchtower rules on the raising and disciplining of children (cf. the 15 December 1961 Watchtower article on teenaged girls in this "sex-crazy world", the 1976 Youth book, and the many articles in the 1970s and 1980s on sexual matters and reproving and disfellowshipping wayward teens).
1950 edition: "But when he again brings his Firstborn into the inhabited earth, he says: ‘And let all God’s angels worship him’ " (Hebrews 1:6).
1971, 1984 editions: "But when he again brings his Firstborn into the inhabited earth, he says: ‘And let all God’s angels do obeisance to him’ " (Hebrews 1:6).
In the 1950s, the Watchtower Society taught that Jesus is to be worshipped (compare 15 August 1941 Watchtower, p. 252) because in the resurrection he was glorified higher than the angels, and thus proskuneo ought to be rendered "worship" in reference to the glorified Jesus and "obseisance" in reference to Jesus in his earthly ministry (15 May 1954 Watchtower, pp. 317-319). This teaching changed subsequently, such that Jesus is not really to be worshipped at all (15 July 1959 Watchtower, p. 421; 15 November 1970 Watchtower, p. 702-703), and the rendering of Hebrews 1:6 followed suit.
There were many, many other examples that I cannot recall, although most of them are fairly minor corrections and fixes of the awkward language in the original translation.