The book of
Isaiah appears to be a layered text. A first layer consists of speeches and
narratives attributed to Isaiah and passed on for generations. Convinced that
the whole was relevant to their situation, later authors made additions to the
received tradition as the circumstances seemed to require.
Isa 34-35 and 40-66 presuppose a set of historical circumstances at a considerable remove from those referred to in the superscription of the book (Isa 1:1). Isa 34-35 and 40-66 contain prophecy whose historical point of departure is different from that of most of the oracles in Isa 1-33 and 36-39.
A majority of
those who have looked into the question see things this way. Among those who do
not and who hold instead that Isa 1-66 is the work of one author, three deserve
mention for the excellent quality of their exegesis: John Oswalt, J. Alec
Motyer, and Barry Webb (full references in the post entitled “An Isaiah Bibliography”).
Those who see
tell-tale signs that Isaiah is a layered text disagree about what is
attributable to Isaiah and what is not. In my view, the author(s) responsible
for Isa 40-66, a work that stands on its own, added Isa 1:27-31; 2:1;
13:1,17-22; 14:22-23; retouched 34:6-17 and added 34:1-5 and 35:1-10 thereto.
In addition, 38-39 was moved from its previous position preceding 36-37 to its
current location in order to serve as a bridge piece to 40-66.
On this view, Isa 1:27-31 was added by an author who heard 1:2-26 against the background of the situation reflected in Isa 56-66. 2:2-5 is the original continuation of 1:21-26. Other scholars have argued along these lines, in whole or in part.
 On 1:21-31 as a complex unity on a par with 1:2-20, see Marvin A. Sweeney, Isaiah 1-39 with an Introduction to the Prophetic Literature (FOTL 16; Grand Rapids: Eerdmans, 1996) 63-65. On 2:2-5 as the continuation of 1:21-31, see Yehoshua Gitay, Isaiah and His Audience: The Structure and Meaning of Isaiah 1-12 (SSN 30; Assen: Van Gorcum, 1991) 35-49. On 1:27-31 as an addition by a Persian period author who hears 1:2-26 against the background of the situation reflected in Isaiah 56-66 and shapes the whole into a new speech announcing salvation to those who refrain from the religious and moral transgressions referred to in Isaiah 56-66, and perdition to those who do not, see Joseph Blenkinsopp, Isaiah 1-39. A New Translation with Introduction and Commentary (AB 19; Garden City: Doubleday, 2000) 187-88. Hugh G. M. Williamson argues that Isa 2:3-4 finds an echo in Isa 51:4-5 and must predate it. Nonetheless he dates 2:2-5 to the same period as 51:4-5 (late exilic) (A Critical and Exegetical Commentary on Isaiah 1-27. Volume 1. Commentary on Isaiah 1-5 [ICC; London 2006] 173-79; 178). The matter deserves to be taken up anew.