There are a number of biological stresses that can severely restrict or harm plant growth and development; but they have little detrimental impact on the benefits provided by atmospheric CO2 enrichment. In the case of weeds, for example, an increase in the air's CO2 content should provide no competitive advantage against non-weeds. Insects will continue to do their damage; but percent destruction will likely not change.
The same can be said about the negative effects herbivory. Plant diseases, on the other hand, should have less of an impact in a CO2-enriched atmosphere of the future, as rising CO2 concentrations help plants become better equipped to successfully deal with pathogenic organisms and the damage they have traditionally inflicted.