have a look at the OP costs for units moving across a minor/major river as per the Hexsides display below - it shows all the info Carl mentioned and note how much the OP costs are - by blowing bridges you can slow down or prevent enemy movement, hinder resupply etc, so I think it's always worth doing. Note also, if the weather for the turn was mud, not even infantry can cross a major river.
In the game system there are 3 types of hex
side terrain: minor river, major river and cliffs.
You can see what type of river hexside is portrayed on the map by right clicking on the hex containing the river and looking at the terrain popup display(and generally the artwork for river hexes gives a good indication if it's minor or major anyway).
To find out more about how rivers affect the game, click the Terrain/CRT button in the Control Panel (bottom left of the main game display, the button is hexagon shaped) and click on 'Hex Sides' (towards the bottom left of the Terrain Data display page).
The first thing you do is look in the centre of the chart and locate the transport type icon under the 'OP' column. (You can determine the transport type of each unit by looking at the unit's popup display).
Next, determine what the current weather is. This is displayed in the top right of the main game screen. In the Kharkov campaign, it's mostly 'Dry'.
Now, look under the 'Dry' column and cross reference to the movement type icon in the middle.
Let's use the infantry movement type as an example.
So the readout for that under the Dry column is: 1/8/*
This translates (via the legend at the top of the chart reading '(+) Minor Rivers/Major Rivers/Cliffs' ) to:
+1 OP expenditure to cross a minor river hexside / +8 OP expenditure to cross a major river hexside / crossing a cliff hexside is not allowed.
Another way to quickly identify different river OP penalties on the chart is look at the color of the OP numbers - light blue=minor river, dark blue=major river.
As well, there's a range of hexside combat adjustments in the legend at the base of the table, using colored arrows and asterisks.
So for instance, we can see by the orange arrow icon that attacking across minor rivers in dry weather will result in normal attack factors being used but no tactical shift bonus can apply through that hexside - so there's a good reason to defend behind a minor river hexside, for example.
Even better for the defender is the major river, where the red arrow pointing upwards indicates that attack factors are HALVED when attacking through a major river hex, as well as the whammy of no tactical shift bonus.
Worse again for the attacker - look across at the 'Mud' weather side of the table on the right. The red asterisk at the base of the major river column indicates that NO ATTACKS can be made at all across these hexsides in muddy conditions. You'll also note there's a lot more yellow asterisks in the major river column in mud weather, which indicates no movement allowed unless across a bridge.
So that's where bridges are very useful for your enemy as they negate the effect of rivers if they are intact - so they are very definitely a weak spot in your defense if you are defending behind a river.
Bridge blowing is not automatic but if you are lucky enough to have a unit with the bridge blowing bonus displayed in the unit popup (as per the unit quick reference guide), you will have a much higher chance of blowing the bridge.
cheers
