Can plants suffer from CO2 poisoning?
Short answer
It has been shown that plants may already suffer from doubling the atmospheric CO2 concentration from 340 to 610 ppm, something that might happen during the next hundred years or so based on current emissions.

Background
A popular science website tells us that an excess of carbon dioxide (CO2) reduces the rate of transpiration of some plants. This is so because the stomata, which are the openings of the leaves (Mansfield &amp; Majernik, 1970) and used for exchanging gases as well as water vapor (transpiration) will close when there is too much CO2 in the air, or other polutants such as SO2. As transpiration drops, the water flow from the soil to the leaves also drops, causing a runoff of water.This in turn stalls nutrient uptake. Indeed, doubling the present-day CO2 concentration to 610 ppm does not necessarily lead to increased growth and may in fact inhibit growth due to excess starch formation in the leaves, indicating it's simply stored as backup energy, nothing else (Coviella &amp; Trumble, 1999). It is believed that plants might be near their saturation point and cannot eliminate CO2 faster than they are doing right now.

Somehow plants also become more susceptible to insect foraging when CO2 concentration increases.

Note however, that CO2 tolerances are species dependent. Most research in this arena has focused on common crops. CO2 tolerance in for example cotton plants is low, and starch buildup has been observed in the entire plant, but especially in the root systems and the stem (Hendrix et al., 1994). Other species, such as wheat and rice are less prone to effects of elevated CO2 (source: Nature). 

References
- Coviella &amp; Trumble,  Conservation Biology (1999); 13(4): 700–12
- Hendrix et al., Agricult Forest Meteorol (18994); 70(1–4): 153-62
- Mansfield &amp; Majernik, Environmental Pollution (1970); 1(2): 149-54

Source
- Earth untouched