While the footnotes are hilarious just by themself (no doubt because Bartimaeus is quite the smartass), the fact that they're justified in-universe (Bartimaeus' mind works on several levels of consciousness, so this is his way of putting that on paper).
Pays off as a brick joke in the third book. Where a footnote is cut off midway through by Nathaniel, who is temporarily sharing a body with Bartimaeus, complaining that he keeps being distracted by the footnotes. For once it seems Bartimaeus's boasting was actually true.
Also, in the third book, Kitty gets Bartimaeus's goat by mentioning that the first details she found about him in her research were in "a fleeting mention in a footnote."
Faquarl, for a single, brief instant reveals its true form when in a flock of ravens. Some literally lose their lunch, some drop stone dead, and the rest scatter. Also, before that, a female pigeon trying to court Bartimaeus when in pigeon form.
Jabor bumping his head on the doorway while chasing Bartimaeus and Nathaniel.
Nathaniel's hilariously subverted attempt at a dramatic reveal in front of Kitty in book two. At first, the entire scene feels like it was lifted from a mystery anime. He brushes his Peek-a-Bangs out of his face, but Kitty doesn't recognize him.
Duvall's death. After being arrested, he kills his guards as a werewolf and leaps out the window. So he escaped? Nope, they were five floors up.
Maybe it's just me, but the mental image of a djinn taking the form of a footstool is sporfle-tastic.
There's also the fact that it turned out to be an actual footstool...
Bartimaeus: (talking about Honorius, an insane rogue afrit) He's not going to be the only mad one if we set this lot loose. Look at that djinn over there. Took the form of a footstool. You know, it's weird, but I think I like his style...
Nathaniel: That is a footstool, Bartimaeus. Nobody is using that pentacle.
Hell, Bartimaeus is pretty much a walking, talking Crowning Moment of Funny himself. There's usually at least one in each of his chapters, especially in the footnotes. A good example is him unknowingly using the Rosetta Stone to bludgeon a golem.
Even more funny if you know that a Ptolemy wrote the stone anyway. A relative of Bart's Ptolemy.
Bartimaeus beating up two people... as a field mouse. Made funnier by the fact we don't get to see exactly how he did it.
This gets something of a Call-Forward in the prequel, where Tybalt beats up Gezeri as a green-eyed white mouse, but how he did so isn't shown.
The conversation Nathaniel and Bartimaeus have after Nathaniel is knocked out by trying (and failing) to activate Gladstone's Staff.
Bartimaeus: The magical energies have been gradually ebbing through your system. Your skin's been steaming and the end of each hair's been glowing at the tip. A remarkable sight. Your aura's gone haywire, too. Well, it's a delicate process, ridding yourself of a charge like that. I wanted to wake you straightaway, but I knew I had to wait several hours to ensure you were safely recovered.
Nathaniel: What?! How long has it been?
Bartimaeus: Five minutes. I got bored.
Why is there no love for Nathaniel not realizing he was being held back from Gladstone's staff by a "push" door?
"I know the secrets of the earth and the mysteries of the air; I know the key to the minds of women. (Patently all lies. Especially the last bit.) What do you wish? Speak."
Even funnier once his summoner (Ptolemy) starts asking questions about the nature of demons- which Barty has no idea how to answer. He's so stumped by this line of questioning that his current form (a sand tornado) freezes in shock.
During Bartimaeus's 'visit' to Pinn's, Simpkin mentions cleaning Nefertiti's anklet, meant for the Duke of Westminster's wife, and claims that it bestows great beauty on the wearer. Bartimaeus, who had procured it for her and knew that she was already quite beautiful, mentions that it actually forces her husband to obey her every word, and wonders how the Duke is managing. Two chapters later, Nathaniel encounters the pair briefly - and the Duke is simply described as "exhausted-looking".
In The Ring of Solomon, Bartimaeus's constant quips regarding Asmira's inability to think for herself.
"Thinking again! How it taxed her."
The ribbing that Bartimaeus takes in the prologue of The Golem's Eye for his boasting about having built the walls of Prague, which are easily destroyed. Doubly funny in that the very first boast Bartimaeus makes in The Amulet of Samarkand is that he "rebuilt the walls of Uruk, Karnak and Prague." Triply funny when in Ptolemy's Gate he comments that the battalion of imps that he pressed into service to build them for him had a frightful time.
Bartimaeus's description of the stylites, ascetics who sat upon high poles and summoned djinn to beguile them with temptations to test their resolve.
"Personally, I didn't bother with the temptation bit. I used to tickle them until they fell off."
In The Amulet of Samarkand, Bartimaeus gives Nathaniel a good dunking in a river to wash the grime off him before they continue their journey to the estate of Simon Lovelace. When he surfaces, he makes a sort of grunting, which Bartimaeus chooses to interpret as a request to be dunked again. "Boy, you are thorough."
The sequence in The Ring of Solomon in which Bartimaeus reveals that A.) he's still alive and B.) he's snatched Solomon's ring. First, after hearing Solomon express disbelief to Asmira that a "mere djinni" could have helped her in breaking into his private chambers, he reveals himself as "a mere djinni who, while you two were chattering away like fishwives, has got himself a ring." Then, when Solomon fails to recognize him in his sand-cat guise, which he's never seen before, he gives his name as Bartimaeus, only for Solomon to still be stumped. Bartimaeus, aggravated, then reverts to a previous form - a pygmy hippo in a skirt that's intended as a comic reference to one of Solomon's numerous wives, specifically the one from Moab. Solomon never does catch on to the reference, but he does finally recognize, with a shock, the djinni who previously made fun of him and disrespected the sanctity of his temple.
In The Ring of Solomon, Bartimaeus provokes his fellow djinn under Khaba the Cruel to bickering and Khaba responds by thoroughly whipping them with his essence flail. Afterwards...
Bartimaeus: I think he forgives us, Faquarl. Look, he's smiling.
Faquarl: Remember, Bartimaeus, we're upside-down.
Bartimaeus: Oh. Right.
Bartimaeus's list in The Ring of Solomon of things that aren't allowed in Solomon's Jerusalem. They include eating guests of Jerusalem, fighting, devouring servants, running in the corridors, cursing, drawing rude stick figures on the harem walls, causing unpleasant smells to permeate the kitchens, and spitting on the upholstery. And these are just the things that he's been specifically told off for doing.