Examples of dumb divisions? I think it would be hard to go wrong with 3 INF + artillery or anti tank guns as SU.
Unless you are expecting a huge tank rush, 3xINF 1xART tends to be far better to build than any 3xINF 1xAT. However, no, neither of those untis are bad; in fact, they are very standard as "line infantry" divisions.
There are some obviously crazy setups... 1xMIL 1xSHARM 1xMP 1xENG would certainly be insane.
Other, more "reasonable" looking, but nonetheless iffy divisions, however, tend to end up like this:
A) 2xINF 2xMIL
-- not helped by the fact that some countries actually start *out* with these types of formations. The logic is that the MIL are there as the cannon fodder for the INF, but the reality is that the IC/LS investment to make these isn't efficient. Choose one or the other (INF or MIL), and just go with those. If you already have a number of both, rearrange them into their own divisions, and if need be, put them in the same province (their combined defensiveness/toughness will still be applied as long as they are both in the same fight). the few countries that would benefit from both types at once, unfortunately, don't tend to have the LS needed to keep both researches current, while doing whatever else they need to.
B) 2xARM 2xINF
-- Again, some countries start with things like this, so to the novice, it seems like "if the AI does it, it must be smart". Also, since this gets the CA bonus, it looks liek it's "smart". But due to the INF detracting from the speed of the ARM units, 1/2 of this type of unit's usefulness is being eliminated. If you want to mix armor and infantry, use MOT or MECH, not INF (exception: HARM tends to be slow enough that INF can meld with it decently)
C) 2xINF 2xMOT
-- thank the starting JAP forces for this monstrosity. All of the problems as the ARM/INF combo above, and this unit doesn't even get a CA bonus as a saving grace. When playing as JAP, find your starting MOT brigades, and IMMEDIATELY de-attach them from the INFs.
D) 1xINF 4xART
-- popularized by the forums, this divsions brings a whole lot of pain down on single provinces, when you stack huge quantities of them in a single breaching attack. What is overlooked by many who read this, however, is that outside of the "breach overload" attack, these units have very low individual survivability, are very susceptible to losses by Airstrike, and cause havoc to your supply lines. So unless you have a VERY SPECIFIC plan for these types of nonfrontage-heavy divisions, you will want to stay away from them.
E) 1xGAR
-- another "good in theory" brigade, the concept here is that by lining areas (especially coastlines) with single brigades, you will be alerted to any landing/invasion before the attackers break into your backfield, and since GAR has better defensiveness than MIL (while still being very low on Officer needs), they will hold up "longer". However, their "longer holdout" tends to be on the order of 2 hours, and once they DO run, they will be lost, since their pitiful speed prevents them from escaping before the invaders push just 1 more province. If you want to line a coast for invasion-alert purposes, 1xMIL is a better choice, straight up. GARs are good for provinces that you actualy want to put up a fight at (at which point you want them to have some bite, like 2xGAR 1xART 1xAA), and where retreat isn't really an option (major ports, islands, and placing single GARs inland on IC/resource heavy provinces to prevent a bunch of 1xPAR auto-captures). However, due to the AI getting flummoxed by shoreliens full of GAR, some people tend to use this as novice GER players, see it work, and then become attached to them.
F) 1xX 1xMP
-- as of this version (3.05), you cannot reduce the revolt risk in Annexed provinces, which means the only use MPs have is in "occupied" territory with high-revoltrisk laws passed. Not that they AREN'T good in those situations, mind you, but those situations tend to be so few as to make widespread MP building a bad idea.
G) #xX, 1xENG
-- ENG are really good at helping in VERY SPECIFIC instances. Across rivers, into forts, into jungle/marsh... however, the number of times you will actually have to do that is low enough that putting ENG into your divisions organically is a major drain on resources. Having a few ENG in, say, your HQ "divisions", which you then split off and reattach to divisions that will be -making- these types of attacks, is a good idea, if you can handle the micromanagement. But if you DONT like that level of micromanagement, don't just "add ENG to everything". It's far too huge a drain.
H) 3xMAR/3xMTN 1xART
-- While DEFENDING, the ART mixes nicely with these specialized divisions. However, when ATTACKING, the ART gets substantial penalties in the types of provinces these untis are designed to attack *into*, making them a REALLY bad expendeture of resources. And since most people don't *defend* with MAR/MTN...
F) 3xMAR 1xENG
-- MAR already have a zero (with tech) penalty on amphibious assaulting. The only time you should consider ENG to go with them is if you are planning to amphibiously assault someplace with a high Fortification presence. Otherwise, if you just want more "oomph", forget the ENG, just add another brigade of MAR.
Do note that the above divisions are "iffy" to create, but that doesn't mean they aren't "effective". Just that a lot of the "less common" creations tend to require specific knowledge of the game, and specific world situations, to be worth their cost.