It's worth getting a professional view on what work needs to be done to your roof. if tiles are falling off, flaking, or bits are breaking off, it could mean they've come to the end of their life. If just a few units are showing damage, individual replacement will probably suffice. If its a lot more than that, it's usually best to re-do the entire lot, as you can expect the rest of the roof to fail within a few years.
If you notice a dip or curve in your roof line when viewing it from the street, it could suggest the timber rafters or trusses are no longer able to support the weight of the structure. The best way to tackle this is to remove the tiles from the affected area so you can reinforce or strengthen the timber.
If your property is positioned close to trees, the roof is likely to gather moss over time. It shouldn't affect the performance of the tiles, but you may wish to remove it for aesthetic reasons. Don't use a jet wash for this, as it can cause damage. Remove the growth using a broom. After you've swept the surface clean, you can apply a fungicidal wash to try and prevent the reappearance of moss and lichen in the future.
Traditionally, certain roof tiles - such as those used at the ridge - were bedded in cement mortar and pointed to hold them securely and keep out rainwater. If the pointing is poor or failing, the only solution is to remove and refit. Dry-fit options are now available for verges, valleys and ridges. These are mechanically fixed and ultra-low-maintenance.