The actual strength or weakness of the case will play itself out in front of the finder of fact. The prosecutor's perception of the case's strength does not change the strength of the evidence presented. Introducing the rejected plea agreement for the purpose of showing that the prosecutor thought the case was weak is asking the fact finder to substitute the prosecutor's judgment for his/their own. The prosecutor's perception adds nothing to the actual evidence and has a substantial risk of prejudicing or misleading the fact finder by inviting him/them to adopt the prosecutor's perception rather than coming to a conclusion based solely upon the facts.
The rejection of the plea offer as proof of the defendant's innocent state of mind is problematic. Anyone who has done defense work has seen defendants turn down all sorts of favorable deals for reasons other than innocence. Among the more unusual ones I ran across were the beliefs that mispelling a name on an indictment meant the prosecution could not convict and an abiding belief that the UCC denied the Commonwealth of Virginia the ability to prosecute for criminal failure to pay child support. More common are defendants who don't believe certain witnesses will testify against them; defendants who don't want to do any time (they will turn down 6 months despite being told they will get 2 years if they go to trial); defendants refusing the plea offer today because it would require them to go to jail today (in effect buying an extra couple months on the street with years in prison; defendants who feel like any conviction will destroy their lives/jobs; &cetera. Often, the choice to reject the plea offer and go to trial is irrational. Professor Miller even acknowledges this phenomenon:
It is well established that guilty defendants as a class are unusually prone to risk taking because, inter alia, a criminal history suggests a preference for gambling, just as it suggests that the defendant fears punishment less than most people. Conversely, risk aversion is a much more plausible assumption where innocent defendants are concerned (especially those with relatively clean records). Therefore, critics…claim that plea bargaining coerces a significant percentage of innocent defendants to convict themselves in exchange for a certain, reduced penalty.With all this in mind, there is no basis for stating that rejecting a plea offer is indicative of either a belief in innocence or actual innocence. In fact, per Professor Miller's statement supra it appears that rejecting a plea agreement actually tends to show guilt more than innocence. With that in mind, offering the rejected plea offer as proof of the defendant's innocence has a strong potential to mislead the finder of fact.
Under both possible uses of the rejected plea agreement the potential toward prejudice and misleading the finder of facts is greater than any actual evidence putatively to be found in the offer.