What are some good examples of Burgess expressing his own personal agendas in the text?
An example of one agenda that it might be said that Burgess is advocating is the reasons youths have for running away from home and braving life on the street and as squatters. Tar and Gemma are in the backseat of a car in a private garage waiting for Barry. Gemma declines Tar's request that she come with him to run away but in her thoughts, she can see the reason for Tar's decision to leave home written in brutal colors across his face:
The latest [reasons] were painted on his face, too. His upper lip swelled over his teeth like a fat plum. His left eye was black, blue, yellow and red.
Thus Burgess, from the very start of his novel, lays out the parental reasons that some youths have for taking on life as outcasts and strugglers: running away to the streets seems far better to their young minds than being maltreated by the ones sworn by blood relation to care for them, nurture them and love them.
Another agenda Burgess might have, along with eliminating blame from the street youths, is that of describing life on the street in full and accurate detail, perhaps to change, among other things, social perceptions of squatting practices.