οὗτοι, ὦ ἄνδρες Ἀθηναῖοι, <οἱ> ταύτην τὴν φήμην κατασκεδάσαντες, οἱ δεινοί εἰσίν μου κατήγοροι.
The entire underlined phrase is the predicate, and the puzzle is the bold-faced εἰσίν — this is the verb, smack in the middle of a noun phrase. In English it'd be like saying "the small is dog mean" instead of "the small dog is mean." Well, not exactly, given Greek word order, but it's still a bit of a surprise. The enclitic μου is less a surprise, and a number of other enclitics and postpositives could appear in the middle of a noun phrase without anyone but rank beginners batting an eye (δέ, γε, κτλ.) I already knew forms of εἰμί, including εἰσι(ν), are enclitic. I hadn't fully appreciated that they can be postpositive. Sir Kenneth Dover (Greek Word Order, p. 13):
(xi) The verb εἰναι cannot be classed as q without many qualifications and reservations, not all of which admit of a satisfactory classification. εἶναι as a copula tends, in most authors, to be treated as q; when it is first word in a clause, we import into its translation nuances which the context does not always demand and sometimes scarcely justifies. I use the symbol Mq for εἶναι in its copulative sense.
He uses q to mean postpostives and M to mean non-prepositive, non-postpositive "mobiles," mostly what we'd consider content words (nouns, verbs, etc.). He invents a special sign for εἰμί to indicate its dual status as both mobile and postpositive. Nonetheless, it doesn't seem to fall in the middle of noun phrases very often. Though I didn't search all of Plato, I did check the Republic where I found only one case that seems similar, with an articular infinitive phrase (just a snazzy noun phrase, really), 339c:
τὸ δὲ ὀρθῶς ἆρα τὸ τὰ συμφέροντά ἐστι τίθεσθαι ἑαυτοῖς, τὸ δὲ μὴ ὀρθῶς ἀσύμφορα; ἢ πῶς λέγεις;
"Correctly" then is to lay down [laws] for their own advantage, and "not correctly" their disadvantage? Or what did you mean?
This was an upsetting find. I had first assumed that the odd placement of εἰσίν was due to the danger of garden path confusion, where the participle phrase might be construed as the predicate if the verb went after the demonstrative or the participle. In the Republic sentence other word orders are possible which could accomodate ἐστι outside the noun phrase. In my somewhat random searching of other texts I finally found a magnificent example from Aeschines, Against Timarchus 117:
ἔστι δ᾽ ὁ μὲν πρότερός μοι λόγος προδιήγησις τῆς ἀπολογίας ἧς ἀκούω μέλλειν γίγνεσθαι, ἵνα μὴ τοῦτο ἐμοῦ παραλιπόντος ὁ τὰς τῶν λόγων τέχνας κατεπαγγελλόμενος τοὺς νέους διδάσκειν ἀπάτῃ τινὶ παραλογισάμενος ὑμᾶς ἀφέληται τὸ τῆς πόλεως συμφέρον. ὁ δὲ δεύτερός ἐστί μοι λόγος παράκλησις τῶν πολιτῶν πρὸς ἀρετήν.
My first point is anticipation.... My second point is exhortation...
A compliant corpus is so agreeable. Here we have perfectly parallel, contrasting phrases of the sort Greek dearly loves, one with an expected use, one with an intruding ἐστί. I've been a big fan of the work of the Dutch classicists investigating Greek grammar from the standpoint of Functional Grammar, especially Helma Dik's work on word order. When I saw the Aeschines example I was immediately reminded of the paper On Unemphatic “Emphatic” Pronouns in Greek: Nominative pronounsin Plato and Sophocles (APA abstract and handout). Unfortunately I'm really out of my depth here, in that my knowledge of Functional Grammar is fairly superficial. I have a basic understanding of its operation at the level of the clause. What I don't know is if the Topic-Focus elements are recursive and one can reasonably speak of Focus in a phrase part of a larger clause — because right now I'm pretty sure the intrusive forms of εἰμί indicate Contrastive Focus on the word they follow. What I'm not sure about is whether this Focus motivates, or is motivated by, the placement of the copula.