Jack believed that Bob said that Nancy saw Bill drove fast yesterday.
Whether there is an error in this sentence or not depends on which meaning of see the writer intends to convey.
The verb see can take different types of Complement. The most common Complements are: a noun phrase, a content clause (just a normal tensed clause with no gaps in it), or a noun phrase plus non-finite clause:
- Nancy saw [Bill]. noun phrase
- Nancy saw [that Bill had been there]. content clause
- Nancy saw [Bill] [steal the money]. noun phrase plus non-finite clause
In its most basic meaning, the verb see means something like: to view with the eyes. (See definition 2 here). This is the meaning of this verb in examples (1) and (3) above.
Notice, though, that example (2) is different. It means something like to become aware of something or to understand something. In example (2), Nancy did not witness Bill being there, but she understood that fact from what she saw. When the verb see takes a content clause as a Complement, as in example (2), it normally has the become aware of something/understand something type of meaning.
Content clauses in English
Content clauses in English are often introduced by the word that. However, in most situations it's possible to omit this word. In fact, we can always omit that when the clause is a complement of a preceding verb1. So the following pairs of sentences mean exactly the same thing:
- Nancy saw [that Bill had been there].
- Nancy saw [Bill had been there].
- She realised [that she was losing].
- She realised [she was losing].
- You insinuated [that I was lying].
- You insinuated [I was lying].
- I think [that she loves you].
- I think [she loves you].
Notice that the verbs in these clauses are all tensed.
See someone do something
The noun phrase plus non-finite clause—or see someone do something—construction is used when the speaker wants to describe what event or situation was directly witnessed by the Subject of the verb see. If the noun phrase is a pronoun, it is accusative, not nominative. Notice as well, importantly, that the verb in the subordinate clause is in the plain form (sometimes called the bare infinitive). It cannot be past tense, and it cannot be present tense2:
- *I saw him stole the money. [ungrammatical, past tense verb]
- I saw him steal the money.
- *I never see him eats. [ungrammatical, present tense verb]
- I never see him eat.
The Original Poster's sentence
Let's say that Nancy works at a haulage company. Her job, is to check the tachometers on the lorries (a tachometer is a device that measure the speeds that drivers were driving at and how far they drove). Now, let's say that Jack reported Bill for driving too fast yesterday - when, in fact he didn't. Jack's excuse is that it Bob's fault. The reason for this might be that:
- Jack believed that Bob said that Nancy saw Bill drove fast yesterday.
Now a different situation. The reason that Jack made the report this time is that Bob and Nancy had been at the pub. Bob subsequently tells Jack that Nancy witnessed Bill speed away from the pub in his lorry. In other words:
- Jack believed that Bob said that Nancy saw Bill drive fast yesterday.
Both of these two example sentences are completely grammatical. However, out of context, we might believe that the author of the Original Poster's sentence really intended a meaning like the one in the second example - even though they used the grammar in the first sentence. Why? Well, the author has used the word that at every opportunity, apart from in the very last clause. This might make us think that this is because the following clause is non-tensed and so cannot take the word that. Another reason to think this is that out of all the potential thats in this sentence, the one in the last clause would be the most important because it would make clear what the speaker intended.
However, there is no way of knowing what a speaker of a disembodied sentence was aiming at. Presumably, we must regard a potentially grammatical sentence as grammatical. If this is an example from a test, it is a badly devised one. The test writer could easily have avoided this problem if they had used a pronoun instead of the name Bill.
- *Jaqueline believed that Brenda said that Nancy saw him drove fast. (ungrammatical)
- *Jaqueline believed that Brenda said that Nancy saw he drive fast. (ungrammatical)
These would have been ungrammatical versions of the following examples:
- Jaqueline believed that Brenda said that Nancy saw him drive fast.
- Jaqueline believed that Brenda said that Nancy saw he drove fast.
1. The one exception being when the verb is the verb would: I would that you were here.
2. If the person only saw part of the event in progress we can use a non-finite participle instead of the plain form: Nancy saw Bill stealing the money.