Chapter 2 addresses a warning about neglecting our salvation because we have such a great and powerful message from God himself. Another notable verse is the reference to God putting all things under his [Jesus'] feet which is a reference from Psalms as well as being found in 1 Corinthians 15:27 ad Ephesians 1:22.
As a the author continues to set up his account of Jesus is in Chapter 3 he compares Jesus with Moses, whom Jews think of as being the greatest prophet, which is especially interesting when you consider that Moses said a prophet would be risen up who would be like him but greater. (See Deuteronomy 18:15). Therefore, the author spends chapters 3-5 showing, using Old Testament themes, that Jesus is the new High Priest, and comparing the believers to the Jews who were under Moses (a theme also present in 1 Corinthians 10).
Hebrews 6 speaks about leaving behind the elementary doctrines of things like washings, laying on of hands, and the resurrection. After this and a warning about falling away, the Epistle focuses on the certainty of God's promises using the life of Abraham which he leads into the obscure character who, like Jesus, is the prince of peace, and king of righteousness. Further, this character provides Abraham with bread and wine which is a likely allusion to the Eucharist that would be instituted by Christ in the New Testament, and Abraham gives him an offering (tithe). The author then in Chapter 7-10 speaks of this new and better covenant on account of what Jesus has done using plethora of Old Testament language.
Again these themes are reminiscent of themes common through out the Old Testament which have a heavy emphasis on the New Covenant obtained through Jesus' blood. However, it is also true that Paul was the Apostle who seems to have focused the most on the New Covenant through the cross.
Interestingly, another use of Old Testament imagery to further Christology is found in Hebrews 10:22 there is a particularly interesting point which finds its parallel in Ezekiel 36:25 where it says "I will sprinkle clean water on you, and you shall be clean from all your uncleannesses, and from all your idols I will cleanse you." Again, as elsewhere, we see Jesus as the fulfillment of Old Testament prophecies, in this case, it seems it is through the cross and his institution of baptism both common themes in most of Paul's Epistles (See Titus 3:5-7, Romans 6, Ephesians 5:26 etc.). Further, in chapter 10 the author speaks of us of us entering the holiest place through the curtain, i.e., Christ. It is possible this is also more Old Testament imagery as the tent where the Ark was held during the Exodus had a curtain made from the skin and hair an animal, and it was stained red (Exodus 26). If this is a Christological connection, it would show that we can enter the holiest place through what Jesus has done upon the cross.
Next, the author speaks about faith in Chapter 11 specifically going into a long list of Old Testament examples of faith. Including a reference to people trusting in a better resurrection which seems to mirror a story from 2 Maccabees 7. The Epistle then speaks about throwing off the weight of our sin and running this race in 12:1 (see also 1 Corinthians 9:24-27) and about Jesus' willingness to endure the cross for us which is a common theme throughout the Old Testament and especially in Paul's epistles.
The letter concludes with encouragement to endure and train our bodies that we may present ourseleves as living sacrifices to God (see also Romans 12:1-2). And with a final greeting in which Timothy, one of Paul's closest co-workers in the gospel, being mentioned as being released.
Thus, while there is plenty to argue against Paul's authorship there seems to be a significant amount of common images and argumentation style compounded by the Ante-Niuean witness of Paul being the Author that if it was not, in fact, Paul it must clearly have been someone who knew him and his epistles very well.