The Evidence Would be Admissible.
Under the so-called "good faith exception" to the exclusionary rule the evidence would probably be admitted over Bob's objections in both cases mentioned in the question. Recent US court decisions have limited the exclusionary rule when police officers reasonably but mistakenly believe that a valid warrant exists, and find evidence acting under such an apparent warrant. However, if there is good evidence of intentional falsification by the police, the exception will probably not apply.
As to the second case, where Bob is home and protests that an error is being made, police are not required to, and often do not, accept much that suspects or subjects of warrants say in their own defense. If anyone could simply claim there was an error and delay a warrant, perhaps giving time to dispose of evidence, many problems would result.
However, the "good faith" exception only applies where the police reasonably and honestly believe that the warrant is valid, or that probable cause exists. If Bob says something such as:
This warrant is for 1020 Anne street, where Alice Crook lives. But I live at 1050 Albert street. See the house number is 1050 right here. There must be a mistake.
then a reasonable officer would probably double check the warrant, and if the officer unreasonably fails to do so, the search might later be suppressed. But this is going to be a very fact-sensitive inquiry, and none of the cases that I know of on the "good faith exception" rule are exactly on point for this situation. I cannot be sure how a court might rule in such a case.
Leon and Evans Cases
In United States v. Leon 468 U. S. 897, the US Supreme Court created a "good faith exception" to the exclusionary rule. In that case the Court held that when officers make an objectively reasonable, good faith decision to rely on a warrant later held to be invalid, the exclusionary rule does not apply, and evidence found during a search under such a warrant, or in the course of an arrest under such a warren, is admissible. The basic logic is that when the invalid warrant was the result of an honest mistake, suppressing the evidence would have no deterrent effect on future similar mistakes, as no one intended to make them in any case.
In Arizona v. Evans 514 U. S. 1 (1995), this rule was extended to officer who rely in good faith on information mistakenly provided by Court employees. The underlying logic is much the same.
Herring v. United States
In Herring v. United States, 555 U.S. 135 (2009) this exception was further extended to officers who acted in good faith on the mistaken information of other officers. Evidence found in a search incident to an arrest, although there was no valid arrest warrant or other probable cause, was not suppressed. In this case a warrant had been issued but later recalled. however this recall was somehow not properly entered into the database of warrants maintained by a sheriff's office. When a nearby jurisdiction called to ask if there was an outstanding warrant on Herring, they were told that there was one. Herring was arrested, and drugs and an unlawful firearm found. Minutes later the officers were told that the arrest warrant was not valid. Herring was convicted based on the evidence from the search, and the US Supreme court upheld the conviction.
The court wrote in Herring:
When a probable-cause determination was based on reasonable but mistaken assumptions, the person subjected to a search or seizure has not necessarily been the victim of a constitutional violation. The very phrase “probable cause” confirms that the Fourth Amendment does not demand all possible precision. And whether the error can be traced to a mistake by a state actor or some other source may bear on the analysis. For purposes of deciding this case, however, we accept the parties’ assumption that there was a Fourth Amendment violation. The issue is whether the exclusionary rule should be applied.
The fact that a Fourth Amendment violation occurred—i.e., that a search or arrest was unreasonable—does not necessarily mean that the exclusionary rule applies. Illinois v. Gates, 462 U. S. 213, 223 (1983). Indeed, exclusion “has always been our last resort, not our first impulse,” Hudson v. Michigan, 547 U. S. 586, 591 (2006), and our precedents establish important principles that constrain application of the exclusionary rule.
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the exclusionary rule is not an individual right and applies only where it “ ‘result[s] in appreciable deterrence.’
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When police act under a warrant that is invalid for lack of probable cause, the exclusionary rule does not apply if the police acted “in objectively reasonable reliance” on the subsequently invalidated search warrant. 468 U. S., at 922 (Leon). We (perhaps confusingly) called this objectively reasonable reliance “good faith.” In a companion case, Massachusetts v. Sheppard, 468 U. S. 981 (1984), we held that the exclusionary rule did not apply when a warrant was invalid because a judge forgot to make “clerical corrections” to it.
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in Evans, 514 U. S. 1, we applied this good-faith rule to police who reasonably relied on mistaken information in a court’s database that an arrest warrant was outstanding. We held that a mistake made by a judicial employee could not give rise to exclusion for three reasons: The exclusionary rule was crafted to curb police rather than judicial misconduct; court employees were unlikely to try to subvert the Fourth Amendment; and “most important, there [was] no basis for believing that application of the exclusionary rule in [those] circumstances” would have any significant effect in deterring the errors
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the abuses that gave rise to the exclusionary rule featured intentional conduct that was patently unconstitutional ...
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To trigger the exclusionary rule, police conduct must be sufficiently deliberate that exclusion can meaningfully deter it, and sufficiently culpable that such deterrence is worth the price paid by the justice system.
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In Franks v. Delaware, 438 U. S. 154 (1978), ... we held that police negligence in obtaining a warrant did not even rise to the level of a Fourth Amendment violation, let alone meet the more stringent test for triggering the exclusionary rule.
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We do not suggest that all recordkeeping errors by the police are immune from the exclusionary rule. In this case, however, the conduct at issue was not so objectively culpable as to require exclusion. In Leon we held that “the marginal or nonexistent benefits produced by suppressing evidence obtained in objectively reasonable reliance on a subsequently invalidated search warrant cannot justify the substantial costs of exclusion.” 468 U. S., at 922. The same is true when evidence is obtained in objectively reasonable reliance on a subsequently recalled warrant.
If the police have been shown to be reckless in maintaining a warrant system, or to have knowingly made false entries to lay the groundwork for future false arrests, exclusion would certainly be justified under our cases should such misconduct cause a Fourth Amendment violation.
See the Wikipedia article on Herring and this Leagal Information Institute article on the case
