It depends
It really depends on a couple of factors in the campaign.
As mentioned before, if the DM is running published adventures (which presume a standard 4-single-class-characters party), the mixed-class spellcaster will be in some degree of distress (depends on how mix the levels are).
Also, if the campaign style is mostly combat-oriented, the lack of spell "firepower" will become readily apparent.
There are three main issues:
1) access to higher level spells
2) effectiveness of the spells you do have
3) ability to penetrate opponents SR
Multi-classing a spellcaster weakens all three of these factors. Unlike BAB and Saves, the spellcasting ability does not get even a minor benefit from the other class(es) taken.
Arguably, a Fighter's "core competencies" are BAB and Feats, while that of a Wizard is spellcasting. The Fighter's "core competencies" are shared, to some degree, by all classes -- but the Fighter excels in those areas. On the other hand, ONLY a Wizard gets prepared arcane spellcasting (leaving aside PrCs for the moment), and even multiclassing in other arcane spellcaster classes leaves the character with 2 or 3 weaker spell lists. A Fighter who takes some levels of Wizard still gets some BAB, hit points, and Save bonuses, and even some feats. A Wizard who takes some levels of Fighter gets BAB, hp, Saves, and Feats -- but nothing added to his/her "core competency", arcane spellcasting.
The impact of this depends on the campaign. In a "standard" dungeon-oriented campaign, the impact is brutal. The wizard who took 1 or 2 levels of Fighter is one spell level "behind" where s/he should be -- having 3rd level spells when 4th level spells would be best for the challenges faced. And those spells are under-powered, doing 6d6 instead of 8d6, so requiring an extra round or two, or a second casting, to put down some foes. Likewise, as foes with SR begin to appear, the multi-classed caster is at another disadvantage -- s/he is less able to make his/her spells penetrate the SR of the enemy.
Now, in a campaign where the emphasis is less on "dungeon crawls", the multi-classed spellcaster is not as badly off. Also, if the multi-classed character is there to back up a single-classed spellcaster, it is not so bad.
I played a Rogue/Wizard who was originally intended to be mostly Rogue, and who used magic to augment his Rogue abilities. That is a concept which works well; he was a little "behind" on the sneak attack damage and skills, but the spells made up for that. Then the party's "primary spellcaster" died in battle and was not able to be brought back (the player had left the group). Suddenly, my Rogue/Wizard was taking all Wizard levels, trying to get his casting ability "up to snuff". Every fireball was a little too weak, and so on, for the challenges we faced; and I didn't have the spell we needed for many encounters, as it was "1 level higher" than I could use. That campaign was a combat-focused set of dungeon-crawls using mostly published modules. I still had a lot of fun with the character, but I also felt the lack of ability in encounter after encounter.