What arguments are given that Ephesians was not written by Paul? According to the opening paragraph of the article for the Book of Ephesians on Wikipedia, it is not universally held that Ephesians was written by Paul. A source on that site says, 


  Hoehner surveys 279 commentators from 1519 to 2001, finding 54% favor Pauline authorship, 39% conclude against Pauline authorship, and 7% remained uncertain.


What arguments support the claim that Paul did not write the book of Ephesians?
I am aware of four lines of evidence frequently adduced:


Greek syntax and vocabulary

Even a casual read through Ephesians in Greek shows it to be different from the undisputed Pauline letters.1 Despite their sometimes complex argument structure, the Greek of the other letters tends to minimize the complicated subordinating syntax of Classical Greek. Ephesians, on the other hand, is known for its extraordinarily long sentences, especially one encompassing verses 3-14 of the first chapter.2  The vocabulary is also different. There are 116 words in Ephesians not found in the undisputed letters (Furnish). 

Of course, one can argue that Paul used different styles for different occasions. Scholars have quantified things like sentence length and comparisons of vocabulary to show that the difference between Ephesians and the undisputed letters is greater than the difference typically seen among works by the same author. This becomes very technical and beyond the scope of this answer (and beyond the grasp of this writer), but the conclusions are generally seen to favor distinct authorship.
Theological viewpoint

These arguments are manifold. The most substantial concern elements of the eschatological perspective presented in Ephesians which are seen to be in conflict with Paul's stated views elsewhere:   


In Ephesians, there is no mention of Christ's expected return.
In Ephesians, believers have already been "saved" and resurrected with Christ (contrast Eph. 2:4–8 with Rom 6:5).
The concern for social order in Ephesians (5:21-6:9) has been considered inconsistent with 1 Cor 7:31 and Rom 13:11–12, in which the end of the age is imminent.   


There are many other minor points. A sampling of those which can be exemplified succinctly:


Christ is viewed in Ephesians as the "head" of the church, distinct from other members of the "body" (contrast Eph 1:22 and 1 Cor 12:21)
Ephesians seems to work with a presupposition that controversy over the law is a thing of the past (2:15), a clear and present concern in other letters, one considered by some to have not been overcome within the career of Paul. 

Portrayal of Paul

The basic idea is that Ephesians portrays Paul as a particularly holy man among the apostles (contrast "earthen vessels" 2 Cor 4:7). He is also seen as the apostle to the Gentiles. (Eph 3:8 is apparently interpreted as a bit of false modesty, as opposed to 1 Cor 15:8-9.)
Dependence on Colossians

Ephesians appears to borrow heavily from Colossians.  If Paul wrote Colossians (not universally accepted by any means, but generally considered in the relevant circles to be more likely than Pauline authorship of Ephesians), it is seen as unlikely that he would borrow from himself in this way. This is considered evidence for an imitator. 


The summary above is organized according to and largely dependent on the references included below. For those who find it relevant, the author of the first concludes that the evidence is


  neither strong nor harmonious enough to invalidate the judgment of tradition.


The author of the second finds the evidence inconclusive. 



References 


Markus Barth, Ephesians 1-3 (AYB; YUP, 1974), 36-41. 
   


Victor Paul Furnish "Ephesians, Epistle to the" in Anchor Yale Bible Dictionary Ed. David Noel Freedman (Doubleday, 1992), 2:539-544.
   



 1. Here I include: 1 Thessalonians, Galatians, Romans, 1 Corinthians, 2 Corinthians, Philippians, Philemon. I'm sure there's no such thing as "undisputed", but this is standard use of terminology.
  


2.  The beauty of which should constitute adequate motivation for all interested parties to learn Biblical Greek.