Well, the short-term effects are quite easy to identify. Both Beatrice and Benedick are made to believe that the other is in love with them. Thus we can see that Don Pedro was successful in his attempt to, as he puts it in Act II scene i:
...undertake one of Hercules' labours, which is to bring Signor Benedick and the Lady Beatrice into a mountain of affection th'one with th'other.
However, whilst it is clear that this scheme has found success, and that the short-term impact of this is rather amusing for all concerned, as Benedick and Beatrice, who had previously been bitterly opposed to each other, now find themselves in the same state of love that they had both deplored, there are other less pleasant long-term consequences. Note how in Act IV scene 1, the relationship of Beatrice and Benedick forces Benedick to agree to "Kill Claudio" because of the way he has wronged Hero, her cousin. Thus their union creates a problematic situation that is only resolved by the exposure of Don John and the way that Hero and Claudio are brought back together.