When Mass Effect was first released, one of its highest selling points was its adaptive gameplay. Any and every choice protagonist Commander Shepard made would have an impact throughout the story, into the sequel, and until the end. Naturally, it was assumed this included hitting every possible side quest in anticipation of what effect it may have in the future of the story.
However, with Legendary Edition now out, it's clear that some missions do not require the attention of the newly-appointed Spectre. They are little more than time-sinks, excuses to prolong the game but don't meaningfully impact the story.
Espionage Probe
Acquired by hacking a terminal in Zhu's Hope, this side mission is taken up due to suspicious supply drops in the area. There are no flourishing colonies or military installations, so it's odd that rations are being delivered here. iral Hackett will also inform the crew that a sensitive Alliance probe has disappeared here, adding some gravity to the situation.
As it turns out, the probe has been seized by a turian extremist, who seeks vengeance against humanity for thwarting the Skyllian Blitz. He has activated the probe's explosive, but Shepard disarms it before eliminating Haliat and his crew. Haliat is never mentioned again. Skipping this mission bears no consequence as the sensitive information on the probe is never brought up in later games.
Find Dr. Saleon
Some missions give Shepard some insight into their squad mates' backstories, but they mean very little if there is no impact on the story. Garrus brings up a cold case he once worked on regarding a salarian geneticist performing illegal experiments on people. Despite his superior shutting the case down, Garrus continued to search. He eventually finds the fugitive's ship and asks to hunt him down.
Dr. Saleon is nowhere near a tough opponent for Shepard or their crew and can be taken out in one hit. However, it turns out that it was not all that important as the salarian is instantly forgotten and remained as such for the rest of the series. If this mission goes incomplete, Garrus won't make a fuss, and the game carries on as though he never asked.
Family Armor
Tonn Actus was a turian warlord who fought in the Krogan Rebellions. When the krogan were quelled, Actus commandeered the Urdnot family armor and kept it as a trophy in his bunker on Tuntau. Wrex requests Shepard help him retrieve this item that rightfully belongs to him.
Family Armor is another backstory mission, and it doesn't tell much. Unlike Garrus' mission, however, Shepard does unlock one bit of extra dialogue with crewmate Wrex, though it's nothing they won't learn In Mass Effect 3. In fact, in the third game, Shepard seems ignorant of Wrex's relationship with his father whether the armor was retrieved or not. Best not to waste the Spectre's time.
Galaxy Collection Items
Many artifacts can be found scattered about the galaxy and collected, but only two of them have any real significance beyond experience points and credits. The ones that are just glorified wastes of time are the Prothean Data Discs, Turian Insignias, and the two-part Locate Signs of Battle. The data discs, as the name implies, are a last source of Prothean science and culture, insignias are signs of lost turian colonies, and "Signs of Battle" refers to the League of One medallions and salarian ID tags.
These items provide some interesting lore and history that predates the founding of the Citadel Council. However, none of them progress the story, and none of them mean anything to the follow-up games. Shepard can rest easy knowing they don't need to hoard junk aboard their ship.
Abandoned Mine
Acquired through detecting an anomaly on the planet Aequitas, which can only be found after purchasing star charts from Baria Frontiers on Illium. After scanning the planet, EDI informs Shepard of the anomaly which is later revealed to be a Reaper artifact. All of the miners have succumbed to indoctrination and turned into husks that attempt to terminate Shepard and crew before they can reach the artifact.
While similar artifacts had been seen in Mass Effect 1, none of them were significantly connected in any way other than name. The team never hears or speaks of this artifact again. Not even in the DLC Arrival which shares some similar appearance to the one in the mine. For as much effort Shepard puts into the battle, its importance is so minuscule that it can be ignored as though it wasn't in the mission logs at all.
Eclipse Smuggling Depot
On the planet Daratar, there is a port where Eclipse mercenaries have set up a smuggling operation. Cerberus is very interested in acquiring the supplies stored in the crates, however, the Normandy is easily detected in orbit. The mercenaries abandon the depot and order their YMIR mechs to destroy the crates, leaving Shepard and the crew limited time to salvage what's left.
This mission is a "gift" from Aria T'Loak the Pirate Queen after Shepard uncovers a plot to overthrow her. The lack of importance of this job couldn't have been more obvious if Aria had told Shepard in person--which she does. The literal "take it or leave it" line tells Shepard that this isn't a priority, and realistically, isn't worth the time or effort to pick off YMIR mechs one at a time to maybe salvage a handful of minerals and gear.
Anomalous Weather Detected
This one is a rare geth encounter in Mass Effect 2 and is only accessible after purchasing a star chart. EDI picks up the anomaly while scanning Canalus, noting odd weather patterns and a considerable amount of geth activity. Shepard and crew land on the planet and must navigate a zero-visibility situation as they fight their way through the synthetics and eventually turn off their weather machine.
It's bad enough that Shepard's best weapons are as useful as medieval technology here, but the payoff is very unsatisfying. It is also meaningless. Not only is there no explanation why the geth are messing with an uninhabited world's weather, but there are also no consequences to ignoring their activity in the area. The geth never attempt to use the technology again.
Project Firewalker
Project Firewalker is a massive DLC in Mass Effect 2 where Shepard and the crew investigate a missing ship, lost data, survey sites, Prothean artifacts, and geth activity. A new location unlocks after a previous mission is completed, with the crew spending most of their time in the M-44 Hammer exploration vehicle. The objective is to determine the whereabouts of a couple of missing Cerberus scientists.
While the fate of the scientists is eventually discovered and their data recovered, nothing comes of it. Cerberus declares their intent to continue the research despite the scientists' warnings; however, this research data never emerges again, and Mass Effect 3 bears no consequences if this mission is completely skipped.
Cerberus Abductions
Mass Effect 3 missions are a little bit tricky, and Shepard can't really afford to be picky-choosy with which missions to complete and which to ignore as almost all provide War Assets to build towards 100% readiness to battle the Reapers. Even so, not all missions are worth the assets provided.
Shepard encounters an Alliance diplomat on the Citadel arguing with someone about locating his son who went missing on Benning. Coincidentally, Specialist Traynor mentions an active mass abduction happening on that very colony, so, why not kill two birds with one stone? Aside from bringing closure to the diplomat, which gives zero war assets, there is never any closure regarding the abductions as Cerberus itself condemned the action. It's an incomplete story with minimal payoff that Shepard can choose to skip altogether.
Cerberus Fighter Base
This mission requires Shepard to return to Noveria for the first time since Mass 1, as Cerberus has established a base to launch its fighters on the far side of the planet. Shepard is tasked with disabling a security to allow the Alliance to destroy the base without being taken out by Cerberus' anti-air defenses. This is done in four grueling steps ending with the demolition of an Atlas Mech.
Of course, Shepard can save themselves the trouble and ignore this mission as it makes no impact on Cerberus' military strength either positive or negative. Shepard might miss out on a small war asset and they may not get those heating unit stabilizers, but they also won't have to battle through waves of Cerberus troops for minimal reward.